The Unopened Barrel (ReTe 10)
R: Touch, D: Mom, T: Part
By touching a container, instantly transport one of the object contained in to to you hand. Casting requisites of an appropriate Form for the object transported are required.
(Base: 4 Transport a target instantly up to five paces (MoH, p.92), +1 Touch, +1 Part)
Not sure if it really needs to be Part, but I think so since you're not transporting the whole container, just a part of it.
Now, would you allow a combo between that spell and Opening the Intangible Tunnel? OtIT says that you can "cast any spell with range greater than Personal on the target", but does that mean you are considered within the 5-pace range of the Base 4 guideline?
Actually, I would not allow the spell as written, since it violates the Limit of Arcane Connections. The target is what you are transporting, not the barrel -- being within something is quite different from being part of something. Changing the Target from Part to Room (meaning +1 magnitude) would allow you to transport all the contents of the barrel (that match the appropriate casting requisites) out of it, but you would not manage to be selective.
The Range should then be brought up to Voice. You are still not touching the Target, unless the Target is "all the contents of the barrel". However, the Target can then be Individual. Finally, unless the barrel has some sort of internal illumination (or is not really sealed), Prying Eyes won't help much.
What if the object transported out is determined at random, or by some other non-selective process (like the top one)?
I was thinking the effect as something like a barrel filled with apples (for example), and that by casting the spell one is transported to your hand. I grant you that T:Room may make more sense than T:Part, but as you mention yourself, T:Room would transport everything out, so it seemed to make sense to cut that down a little if you are only transporting a single unspecified object out.
Now consider the situation of a barrel filled with liquid (say beer). A variant of this spell (either in Aquam instead of Terram, or with an Aquam requisite) might allow you to transport enough liquid to fill your mug without opening the barrel or tapping it. Would the target need to be Group or Part?
As to detecting what's inside a closed container, might not a simple Intellego spell to ask the container what's inside be sufficient? You don't really need to project your senses to do that, there are plenty of Intellego spells that provide information without going through one of the 5 senses, I think. Using a specific sense is usually more of a cosmetic effect of Intellego spells, IMHO.
Asking the barrel would be an InHe effect T: individual which would get you as good a description of the contents as a barrel can give but not let you target those contents. Projecting a sense of your own would be InIm T: room and would give you information as if the relevant sense organ were within the barrel which may be more limited but could potentially be used for targeting.