Q: What is going on with my car? Why does it shut off whenever it wants to?

I just bought a used Suzuki SIdekick- 1997(1.6L) a week ago. My mechanic told me it was a good used car and that I should buy it if I really want it. He checked it and everything. This week, the car starts shutting off so I replace the old battery it with a new one because I noticed it was leaking acid. I thought my problems were over but then the engine starts shutting off whenever I slowed down or stopped; this does not always happen but it is somewhat persistent. Today, I left the car on because I was parked. Once I was ready to leave, I placed my car on reverse and then the engine turned off completely and I was not able to turn it back on until someone gave me a jump start. The battery kept on dying for like 10 min, and then I received another jump start. I wasn't able to drive the car until 2 hours later and the car was ok again and did not stop at all. The battery sensor as well as the brake sensor and the service engine soon sensor pop up whenever they want to.What's happening?

My car has 101996 miles.
My car has a manual transmission.