1) How much Aq salt did you add? Using aq salt to treat wounds and sores is OK. But don't use aq salt for more than 10 days, though. Bettas are sensitive to it, and it can cause internal damage, especially to their kidneys.
2) White tips on the fins are fine. If it looks like regular fin material, just white-colored, it indicates new growth. If you notice dark or discolored areas on the tips, that would indicate rot.
3) White fuzz can be several different things. Does it look like the picture below? If so, it could be columnaris. Columnaris is an opportunistic bacterial infection that can spread quickly. (Ie: it can take hold quickly if a fish's immune system is already overworked from things like poor water conditions, etc.)
Columnaris: a bacterial infection