Q1. Correct. Actually, if you place "a" in front of long history, it would be incorrect as that long history is definite. Q2. An experience and experience (uncountable) are different in meaning. One refers to something that happens and the other refers to the knowledge that you have gained.
erm yes history can be definite. Ahistoryisanaccount ofeventsthathavehappened inthepast. I don't think you should be answering qs if you don't know something as basic as that.