Just paid 1500 for new engine and having problems

Hello. I have a 2003 chevy cavalier. I bought it used and it had 150k miles on it. This was 6 mos. Ago. Nothing sounded off and never had a problem until last week.
I am in the process of getting my engine replaced as I was told that was the problem. Initially, and this was sudden and happened over maybe 3 days, the car wouldnt be idling properly. At first, I noticed it seemed a bit shakey when stopped then noticed that the rpms were going up and down. This increased more and more over 3 days until on the way home from work it sounded very bad and then stalled. Then it would stall if I didnt rev the engine. The next morning it would not start. Had it towed and the original place said took motor head off and there was no pressure in the engine or cylinders. (He, at the time told me the timing chain was fine). Was told I needed a new engine, but this mechanic didnt do that. A friend and I looked at it and the motor head had clearly not been taken off. I towed it to another place and they said it was def. The engine. They installed new engine and said timing chain had jumped and that ruined the motor. Then they were having trouble getting it started. Today they say the fans arent working and this caused it to overheat. (It had never overheated prior or during the only one day it stalled before it wouldnt start). Now they say it needs a new fan and they dont do that so it must be taken someplace else yet again. I should note I have an interlock device installed (blow box for dui) which must be blown into before starting. That was installed 6 months ago. Told that possibly this caused the wiring to the fan problem, as to why it is overheating. However, like I said, it NEVER overheated when I have been driving it, even when it was 90 deg. Out. I am getting so many different things told to me, and I am suspicious as to if it even needed a new motor. The man who installed the interlock device said he was a mechanic and when we started car (6 mos ago) that I was eventually going to need a new starter.(It made a grinding sound right as it turned over). The mechanic that installed the new motor said the starter was fine. I am just suspicious of all of this as it doesnt seem to be adding up. (Except financially, and very quickly) I dont know much about cars, but it doesnt seem right.
Any insight would be more than appreciated. I feel I am being taken advantage of and spending LOTS of money.
Thank you so much