'96 Eclispe downshifting and dying

So, I have a 1996 Eclipse 2.0L automatic and I have been having some serious problems. When my sister gave me the car it had been sitting around for years and when my dad and I got the car back to our house it began idling really rough and low(around 300 RPM). We replaced some parts, got new motor mounts, and it started to run like a decent vehicle. However, a few weeks later it began to drop it's RPMs whenever braking occured, and few days after that began it started to die when coming to a stop. The problems began to build when it started to downshift when braking, even at high RPMs. We've looked at vacuum lines and electrical connections, but we haven't been able to find anything. My dad believes that the car had a turbo on it at one point and that it was raced, but I'm not sure what that could have changed(I'm not really savvy).

Anyone else have these problems? Any suggestions?

sounds like an iac problem.....
try replacing that before going any further.
my eclipse was doin the same thing
b4 i changed it this weekend
just fyi
2 8mm bolts hold it on

and you can check your vin with mitsubishi to see if it came with a turbo