What happens if a weapon breaks in the middle of battles/run out of uses before battle ends...

Well, you're character basically loses the match. As long as the opponent hits, you can't counter. At least, that's how I've seen that kind of fight work out.

My dodge sort of would make it take a while... (If there magic users there uses go down the drain :D)

Is it a human opponent or an NPC? If it's a human opponent, you're screwed, and you have to judge the entire battle until somebody wins, knowing that your character is destined to lose. If it's an NPC, you can just say that you lost, and let the weapon break, but then you can't fight that NPC anymore. Weapons breaking before a win is a lose-lose situation.