One thing that continually confuses me is the reference to "a Finesse roll" in the rules. Now, the rules are pretty clear that most actions require a roll of Characteristic + Ability + Die Roll.
But only once in the entire rulebook do they give an example of what characteristic should be used. That one time is when discussing Creo magic, and the example is an Int + Finesse roll.
Then, the rest of the core rulebook goes on to simply refer to "a Finesse roll" as if that were the most obvious thing in the world. In that case do they mean a roll of just Finesse + Die Roll? Are we supposed to figure out which characteristic applies in each situation?
Aiming requires Perception + Finnesse + die, p. 86 ArM5.
You're right, though that there's little discussion of Finesse in the main rules. In general, you are apparently supposed to puzzle it yourself. Knotting up a rope - F + Dex. Adding speed - F + Quick, I suppose. I can't immediately think of a F + Str roll, but possibly something involving a feat of magical strength.
Finesse is specifically an Arcane Ability, however (meaning that most painters, for example, can't get it), and refers to the use of magic. I think you're adding effects to it that aren't there because of the Ability's name. (Don't have Covenants, can't comment on the knife.)
Painters would use a Craft or Profession or something.
Finesse is relevant to the Stone-Cutting Knife and other similar items presented in Covenants, however. I don't know if Covenants introduced the rule, but according to that book, any magical device whose effect would need a Finesse roll requires a Dex+Fin roll on the part of the item's user. I think it's Dex+Fin anyway, it might simply be the same type of Finesse roll that you'd use with the effect normally were it a spell. I'm fuzzy on it.
Ability rolls can be paired with several relevant characteristic depending upon the circumstances. Finesse's pairing characteristic is dictated by the circumstances. If you are using Creo magic to make something it is Int+Finesse, if you are using Rego Magic to Craft something then it is Per+Finesse. If you are aiming a magic spell that bypasses MR, then it is Perception. If you are fast casting then it is Quickness. The example of the Stonecutter's Knife makes an explicit Dex+Finesse roll for that item only, but it generally makes sense for an item that does something similar and requires the wielder to touch the affected target, otherwise I'd then rely upon Perception.
If I'm an SG and you had just bargained with someone to get something, and you felt you might not have the best deal, I'd probably have you make a Perception+Bargain roll to judge that, but you used Com+Bargain to get to do the negotiation, and you might use Int+Bargain to see if you can sell it for a profit. Some Abilities pair strongly with one characteristic, but the system is flexible enough to allow abilities and characteristics to be combined in different ways. It is why I try hard to specify the ability and characteristic in the request for a roll.
I get the general idea that you pair an appropriate ability to Finesse for each roll. And the Creo/Rego Int/Per rule is a good one. But what about, say, Wings of the Seven Winds? That requires "a Finesse roll." Is it Int because it's a Creo spell?
I'm inclined to let that be Int+Finesse, because you are constantly creating the winds in the direction you wish to go and at the velocity you wish to go. But Perception is just as appropriate due to the Rego requisite to control said winds. I'd let it be caster's choice...
So, I reread that table. The context of that is the Hermetic magic chapter, and specifically one uses Quickness + Finesse for Certamen, and you'll note that all of the rolls around it are for Certamen.