Does it have to be in contact for the duration? If it's got a Sun duration with sunrise/sunset triggers, it would only have to be in contact at those two times, I think.
Based on the spell description for "Purification of the Festering Wounds" I think so. Well. They have to be under constant influence of the spell, which I suppose if it comes from an item I guess they just have to be touching it at Sunrise and Sunset.
Magi of Hermes disagrees. The Bed of Rapid Convalescence (p. 23) has the same effect but requires the patient to be in the bed for the entirety of the recovery period. 
They can probably reach some arrangement.
But RAW states that targets under an effect do not need to remain within range to continue to be under the effect. If it's a concentration spell and the target has moved out of range, the effect continues, but the ability to control it fails. So, the person does need to be in bed at sunrise and then at sunset.
Chalk the bed in MoH up to another issue with MoH...
Vulc is willing to cast Laboratory of Bonisagus for Vocis, if you can come up with the vis. He would also be willing to ask Egon to aid Vocis at some time in the future when needed (and Egon's assistance is equal to Mica's).
His Bargain is 2*2+0bargain-2com = 2. So... maybe Vocis is feeling magnanimous? 
"I'm not very good at this. My... my venditor used to handle these things for me. She could talk a starving man out of his only slice of bread."
Assuming Vocis doesn't totally fleece Vulc for Mica's assistance, we're at 56 +6=62, which is enough to make the earring give +15 to Recovery rolls. 4 = no extraordinary effects.
Having to stay in constant contact with the bed is a stupid idea. Even sick people have to use a chamber pot! But even if they have to stay in contact with the item, an earring circumvents that problem. It's a good idea to make it an item that stays in contact - if it's a pendant or something, it could come out of contact at sunrise or sunset and then be unable to keep up the effect.
I wouldn't go quite that far. 
Nonsense. Your offers are quite generous. As for the...loss?...of your venditor, I would be a poor brother magus to take advantage of such a situation. However, I do have a counteroffer. Nothing that will tax one of your skills, but something more fitting to my mind. You've spoken previously of 'items of quality', one of your Valdarian secrets. While I admit my understanding is limited, I'm under the impression that these are rather simple for you to enchant and may take many forms.
I am approaching the point in Mica's training at which her role within the House must be chosen. I will need another year or two to determine all of her strengths and weaknesses and set her on the path. At that time, I would ask her to choose an item of quality as her reward for her season of service. A first test, if you will, of her understanding of her role within the House and the Order. Would you be willing to enchant an item of quality of Mica's choosing in exchange for her assistance?
Com 1 + Bargain 1 (+ Favors specialty 1) + roll 4 = 7
And in fairness...
Com 1 + Guile 3 (+ Feigning Emotions specialty 1) + roll 1, 7 = 18
I'll explain that one if Vulc can get lucky on Folk Ken. If not, I'll explain once we hash out the bargain. For the moment, Vocis is the very image of magnanimity.
Ah yes, Vocis is very convincing, but you're forgetting about Vulcanus' massive hubris...
"A season of my time in exchange for a season of hers?! You're valuating the time of your apprentice as equal to that not only of a magus, but a magus of my ability?!" Vulcanus looks ready to punch something. "I would certainly have been willing to craft an item for her had you but asked, but for you to insult me so deeply--!" he stands up, with his fists clenched. "Good day, sir!"
And just to be fair, a Folk Ken roll to see whether Vulc thinks Vocis actually meant that as an insult or if he made the insult because he didn't think it through, (or if there was something else entirely he was trying to get at)...
0 Folk Ken -3 Perception + http://invisiblecastle.com/roller/view/4141267/ (but not a botch) = -3.
So Vulc is convinced Vocis was being a snide little Tremere telling him to "Gehe verletzen sich." 
Interesting. It was meant as an insult, but he was a little surprised when Vulc took it as such.
Vocis cocks an eyebrow and remains seated. Oh, you're quite good. I actually believed your 'lost without my venditor' act. I apologize for skipping the discussion of my starving children and shrewish wife. Crafting an item for Mica would certainly be a fair exchange. Would you care to discuss limits, such as Arts or magnitude?
Vulcanus appears visibly confused at most of Vocis' speech. But when Vocis mentions Gemma, Vulc's eyes turn to ice.
"Absolutely not. One extra pawn of vis is sufficient for me to create the item I have planned, without your apprentice's assistance. Her time is not worth more than a single pawn of vis, but mine IS. And if your belief that Micaela is actually my equal" -he sounds REALLY dismissive and snotty here- "actually has any kind of basis, however small, in reality... Then you would be doing her a disservice by not allowing her to make her own items. Now, I believe I already bid you a good day."
(This guy has no Guile and not only does he have no concept of negotiating for services, he finds the idea of haggling for his work to be completely offensive. He genuinely believes people should be begging him to let them throw money at him.)
Really? Oh, I had read it as just standard barter tactics Ah well, even a broken clock is right twice a day.
Resuming Mica is allowed some time to hang out with the "big girls" once in a while, let us presume that Mica casually mentions this incident while [strike]smoking cigarettes in back of the bleachers while cutting algebra class[/strike] they are relaxing in the lounge listening to a group of troubadours (one singer/fife player, a lute player, a drummer, and the fourth plays Latin guitar).
Poor little Vulcanus, always running around asking for the help of this or that person in the lab. For, no matter how great he claims to be, he is never quite good enough to really do anything useful. He can't even make a flying carpet. He came to me the other day, asking me to make an enchantment for him! A thunder hammer effect that was outside his range of capability. All I asked of him in return was for him to make a new flying carpet, and I would even assist him. My God! He was so condescending and insulting! I just had to calm down and told him just to leave.
Seriously? If word gets around that the Pontifex talks about him like that, Vulcanus will leave the covenant, no questions, no warning, no nothing.
Women have a whole secret world that men never hear about, except sometimes when they listen to them talk about other men (but he never knows what they secretly say about him).
And Carmen is using smack talk as a way to open up conversation as to how to deal with Vulcanus. We need to find a way to reign this in. Excessive Hubris is making the character almost unplayable in a social setting of any sort.
And Carmen is still kinda pssd about some nasty and offensive things Vulcanus said.
So it is up to you as a player as to how to deal with it. If you seriously and dedicatedly believe that must be the way Vulcanus reacts if he ever hears, then simply decide that he never hears.
That's REALLY not true. We'd like to think it's true sometimes because they can be frustratingly enigmatic, but in reality women are, in fact, people.
Carmen is also in a position of authority now, and no longer has the freedom to say whatever she wants without it potentially having serious impact on the covenant's future.
His hubris is really not that hard to manage. We've all got that one really fat ugly friend that needs to hear she's pretty. Typical Verditius hubris is not so different.
That's fair. Perhaps while she's stewing in anger she might consider that, as Pontifex, she can't afford to throw temper tantrums anymore, and figure out how to rein in her own self-destructive tendencies.
There's a point at which that would strain the limits of believability.
If word DOES get around, though, the consequences could be a great opportunity for some character development on Carmen's side.
Is this something that Mica would even know about? She's an apprentice, and wasn't party to the negotiations – that was, I think, between Vocis and Vulcanus. If Vocis wants to tell his apprentice that he tried to get her a season working with Vulcanus in exchange for a season of his time working under Vocis, but Vulcanus wouldn't agree, and put whatever spin on it he wants...
And then, if Mica would then complain to the other magi about it...which would be akin (to use Marko's high school metaphor) to going to her English teacher to bitch about her algebra teacher, that's something else.
Um...wow. I don't even know where to start, here, except that this comes across to me as an extremely negative stereotype.
But if this is a conversation that does happen, and Vibria's a part of, I don't think she would exactly have Carmen's back, here.
All people can be frustratingly enigmatic, regardless of gender of the subject or the perceiver. And if you notice, my statement already included a loophole. Humans, by their nature, tend to segregate themselves into "cliques" based upon gender, ethnicity, hobbies, jobs, etcetera. Any individual human may be part of and/or associate with several sub-groupings. Men have their ways too, "Man Law" or "Bro Code" if you will. But we all know that these are merely poetic constructs. All little social groups cross pollenate ideas and information.
She is also quite inexperienced at this, and is no older or wiser than any of the rest of you.
I dis plan a second paragraph digressing into being concerned about Vulcanus and trying to think of ways to reach out to him. But I thought that was getting too emo, so I wanted to wait for the other girls to gossip first 
This is very different. Vulcanus is not a fat & ugly school girl. He is a genius and a master of his craft. My counter analogy would be having a friend who is a mega-famous supermodel hottie and needs to be constantly reminded she is pretty and demands constant praise.
Two unflattering comments referencing her father, one or two inappropriate and unwelcomed sexual comments, and threatening to spank her. Carmen had every moral right to just slap him, and everyone in the theater would have cheered.
However, and this is exactly your point, that would have a quite negative effect, and Carmen would go through a process of self incriminating self reflection as she tried to become a better leader. I am reminded of the character of Nichole Wakefield in "Garden of Rama" by Arthur C. Clarke.
The fact that we are playing wizards in a huge society of wizards strains the limits of believability.
Indeed 
To use your analogy:
He's a genius and a journeyman at his craft, who's half the age of everyone around him. He is good at ONE thing, and yes, he needs to hear that his peers appreciate that, because as far as he's concerned, it's the only thing about him that's worth anything.
I don't know what world you're from, but it sounds boring and I don't want to live in it