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True Lineages introduces a number of "fighting styles", some of which have a special effect if "the attacker lands a succesful blow but declines to do damage". Is such a blow one that penetrates the resistance of the target or one that just penetrates the defense of the target?
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Does a Tremere whose Technique and Form are equal choose which one to double? Or perhaps if they are equal they can double neither, as a literal reading of the rule would seem to imply? (Note that this is a more general question regarding magical focus)
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Can spells and/or magic items affect Certamen directly (e.g. PeVi to weaken an opponent's attack)? Can they do so undetectably (e.g. one can't tell the difference from more powerful duelist)?
Of course.
That will depend on who is looking and what the effect does.
No opinions whatsoever about questions 1 and 2 - especially 1?
My feeling is penetrate the defense. It acts like the feint or similiar in that you get by the defense and pull them into an unbalanced situation to set up the next round. Remember they get to attack back before you get to use that advantage.
If the two arts are equal, you name one to be considered lower. it doesn't matter whether it is technique or form since the effect is the same.
I would say the two involved in certamen can not. They are focused on the combat ritual and the moment they stop doing so enough to cast a spell, their phantasm vanishes and thus they have lost.
Someone else potentiallly could but if they get caught, it is likely to be brought before a tribunal and there will be a new ruling and new high crime. It definately would be fairly noticable that someone had done something to the one effected. After all, they concentration is strong, they are fighting hard and they know their arts and phantasms. It is like giving someone's leg a yet in middle of combat. They might still win but they know someone or something yanked at them.
I think that I'd still let them try if they wanted to. But yes, magi involved in certamen would need to make concentration tests (against high Ease Factors) to maintain concentration on their phantasms at the same time as casting spells. Also they'd need to cast without gestures and words...otherwise it will be very obvious what they are doing.
Performance magic (certamen), anyone? 
Performance magic requires an ability to link to it so I don't think it is option. On the other hand, my mentem expert in my offline saga has subtle,quietx2 as virtues
Certamen depends on Several abilities: Finesse, Penetration, Parma Magica, and occasionally Concentration. Don't know if these satisfy the Performance Magic requirements though.
nope - none of those satisfy the requirements: the (activities of the) ability have to provide either Gestures or Sounds (or both) which can replace the Gestures or Words of Hermetic casting.
To use the Performance Duration the ability has to have an on-going element of performance (gestures or sounds).
Note in particular, that as a meta-gaming consideration, Performance Duration is intended as a replacement for Concentration Duration, so "Concentration" is certainly not intended as a suitable ability!
Penetration and Finesse are only used as (mental) modifiers to other activities;
Parma Magica is performed as a short "ritual ceremony". While you might argue that performance could happen during this, you can't (so far as I know0 do much else apart from performing the Parma ceremony (eg spell casting!) so
a) you could only use PM while performing the ceremony and
b) you can't cast spells then
so it's not appropriate even if you argue the words and gestures of the ceremony might "count".
You could use Performance Magic during Certamen if you sing a song or something similar at the same time. Of course, you are then going to be making Concentration rolls to maintain your phantasm while singing, but you will be able to disguise your spell casting.
I'm not quite sure which aspect you are addressing, but:
Certamen is not spell-casting, so "Performance Magic (Sing)" won't help the Certamen battle itself...
... and you can't cast spells during Certamen battles (?rules say you are unable to? You are "in a trance").
Singing is not part of the ability "Certamen", so Performance Magic (Certamen) still won't work even if you sing... the sound/gesture actions for Performance Magic are specifically the sounds and gestures which are a normal part of performing the activity of the Ability chosen.
There is no ability "Certamen". Thus there can be no more a performance magic(Certamen) than there can be a Performance Magic(sleeping).
I agree with you about Performance Magic, but I don't see any reason why a character can't try to cast spells while participating in Certamen.
Yes, you are in a trance, but that just means that the Concentration rolls to both maintain the Certamen phantasm, and to cast the spell while doing something else, should be against high Ease Factors. So, practically, it might be virtually impossible, but, I don't see why a suitably skilled character can't give it a go.