Macbook air 11'' not working for over a year.

So about 2 years ago my mac wasn't working, The mac, when opened was restarting every time after half way to boot up. later I got to a verified apple store in Egypt called "Tradeline" who identified the problem which was the hard drive was full, in which they replaced the 75 GB hard drive to a 500 GB one which costed about 400 USD or 7000 EGP.

About half a year later the same problem happened again, but this time the hard drive wasn't full, it was about 120 GB out of 500. The problem was very similar, instead of: half way booting up then suddenly restarting and looping, it booted up, asked me for the password (which i typed in) and then loading and the half way load then it closes then says "Your mac restarted because of a problem, Please wait a few seconds or press any key to boot" then when it opens again the same thing happens in a loop. note that about a year ago the battery stopped working which i fixed which later broke again.

I am asking what's the problem with my mac? I get a whole lot of different answers, once when i got to a laptop store they took a look and said "the hard drive is overheating all the time, it looks to me that the hard drive is incompatible with the mac" so me and my family were angry because we spent 400 USD on almost nothing. So me and my mother went to tradeline to complain which they said the problem is not with the hard drive but with the battery. which i think is a lie because it used to work with the battery not working while putting it on the charger. I'd really appreciate a comment on what to do and/or what's the problem.