A question that has come up in our group is how exactly are we able to apply the Feat of X powers? If you use the strength one to increase carrying capacity are you allowed to use it multiple times? When you use Feat of Dexterity to modify a check could you use in in conjunction with an attack using weapon finesse? If anyone could give some clarification on these it would be much appreciated.
This works like any other ability or skill check bonus. It specifically must be either a skill check related to the stat or a stat check (e.g. Break DCs on doors).
Alright, that's what we figured but we just wanted to make sure for the technicality of it. Still though, can you stack them?
Define "stack them." You could certainly choose to have 2 or more of them if you really wanted. They are, however, tied to specific stats and are all circumstance bonuses, so you couldn't activate 2 on a single check and have them stack for the result on a single check.
Could you use feat of strength's secondary ability to increase your carrying capacity multiple times at once?
Carrying Capacity is not a check and, thus, could not be modified by Feat of Strength. You could, however, make a somewhat prolonged check involving heavy lifting (moving a heavy object across the room, etc.)
Feat of strength specifically has a section that says you can apply that +20 to your strength for a number of hours equal to your mythic tier but only for the purposes of carrying capacity. It's in the ability description.
I missed that extra line. That being the case, it's still a circumstance bonus, so you could only have one active at a time.