How many foul balls are allowed before a batter is out?

There is no limit to the number of fouls in the MLB.

The only rules about foul balls is if a batter attempts to bunt with two strikes and the ball is bunted foul, the batter is called out. But there is no limit to the number of foul balls a batter can hit when swinging at the pitch.

This is true. However, the first 2 foul balls that are hit and not caught are considered strikes. After that, there is no limit to the amount of foul balls that can be hit, as long as they're not caught.