What factors are influenced by the ring size (mixin) selection?
Answers below:)
Yes, except if you're consistently using some weird number like 103, in which case you're leaking the fact that every transaction using that mixin might be yours.
In a way, yes, but you're paying for the physical size of the transaction, so if you can afford to stuff the Monero blockchain you can afford to stuff all the others.
Linearly; if a mixin of 3 takes up exactly 1kb in signatures, then a mixin of 6 will take up exactly 2kb in signatures. The actual numbers are a little different, and will be further different with the addition of RingCT, but Monero fees are low enough that you can consistently use higher mixins without concern.
The minimum enforced mixin is 2 (ie. your signature plus 2 others). We will likely raise this with RingCT, as transactions will tend towards 1 or 2 inputs. I'm of the opinion that the minimum mixin for typical cases is around 5, and around 20 for higher threat models.
fluffypony gave a good answer for pre-rct, I will give one for post rct, which is both similar, and different:
A higher mixin means selecting another input that could be the one that's being spent. So yes, in general. Using many inputs can currently show correlations between inputs if you have few of them, but when RingCT is merged, this will be lessened, meaning that a higher mixin will more reliably increase privacy.
Yes. When RingtCT is in, higher mixins will have a lesser influence on transaction size. In other words, for a 2x increase in fees, you can select a much higher mixin than you could pre-rct. This is because the range proofs take a lot of one of space do prove input/output equality, so adding more inputs is cheap in comparison.
Linearly, too. But with a high constant. That is, something like y=ax+b, rather than y=ax.
As fluffypony said. The minimum mixin will likely be increased for RingCT, especially in light of the relative cheapness of higher mixins.
