does light exercise bring more useful muscle then heavy lifting

Yoga would be the best way to go for what your asking.

Breathing heavy has more to do with how well your stamina plays into your lifting sessions. Someone who smokes and lifts light may breathe heavy while an athletic person who is in shape could lift heavy and not breath heavy. Lifting heavy puts stress on your body which is why it builds muscle. Most people can lift light weights and lifting light weights does not demand much stress of your body hence it is not a method used by those attempting to bulk. If you are breathing heavy you should start running or doing light cardio or something.

Well building muscle with a low heart rate builds loose fast muscle. So is 30 minutea or an hour of exercise with a low heart rate better?

well it depends on the person but yes trying to keep a low heart rate would be good for the body in general.

From my experience, it's very hard to not be breathing at an elevated rate just after you finish a set. If you are not, then there isn't much effort being put forth.

As far as useful muscle goes, unless you are on the "juice" or some type of hormone replacement stuff, you aren't going to get all big and bulging.