I tested this using a Vanguard with access to both Cryo Ammo and Incendiary Ammo at the Shooting Range on the Citadel, with an M-3 Predator with a base ammo capacity of 105 (90 + 15 in Clip).

After learning the Rank 5 Incendiary Ammo upgrade for increased capacity, my max ammunition remained the same until I activated Incendiary Ammo. After activating the power, the clip size remained at 15, but my reserve capacity jumped from 90 to 116, for a total of 131 rounds.

I then learned the upgrade for Cryo Ammo. When activated, the reserve ammunition jumped to 116 again, clip size remained unaffected.

No, they do not stack, and Yes, they only work when the Ammo Power is currently activated.

_{Further testing needed: Whether a Squad Ammo upgrade at Rank 4 combined with increased capacity from Rank 5 increases ammo capacity for the whole squad.
Edit:Yes.}

For the most part, nope. No reason not to always have an Ammo power activated.

An exception might be if you are specced into, for example, the final rank of Incendiary Ammo and the explosive effect would be inconvenient for some reason (Perhaps you're trying to snipe a target without blowing up a strategically placed explosive barrel or something.) Those situations should be pretty incredibly rare though.

Ammo Powers will never leave you vulnerable, they will not cost you credits, will not damage your weapons, and will not kill your fish. They will allow you to do more damage, apply useful debuffs, and, with upgrades, carry more rounds.