Long List of Problems, Please give me some input

Alright, so I bought my 95 Z34 (3.4L) about a year ago, and everything was perfect with the exception of the ABS, but that has miraculously gone away. This spring I noticed a problem when I accelerated too fast. This is problem number 1.
1: I gassed it hard to pull out and when the car shifted gears it slipped, the RPMS reved, and the Check Engine light came on. I restarted the car, and everything was find for quite a while. Then this problem began reacurring often, to the point where I couldn't drive a mile or get it out of first gear (auto transmission) without the check engine light coming on and the transmission switching to a gear (probably 3rd) where 60mph=3,000rpm and 80mph=4,000rpm. This is a pain because I get horrible acceleration from a stop, and I can't go over 4,000rpm. Everything is normal again after I restart the car, but when I start driving again, its back. It doesnt always do this, lately its been driving just fine, but I'm sure it will be back. The computer doesn't register any codes, my mechanic has no idea what the problem is. This is my main concern, does anyone else have this problem or any ideas?

Problem 2: Engine idles up to 3500rpm and then drops to near stall when I first start it up. When I put it in drive, the problem goes away, but the idle continues to rev up and down until it finally stalls. Any suggestions?

Problem 3: Low oil light comes on every now and then, but there is plenty of oil.

Other than this, I LOVE THIS CAR. Please help me out, any input is appreciated. Thanks again!

My '96 Z34 (which I sold in '98) did very strange things around 7500 miles, quite similar to yours (I'm sure yours has much higher mileage). It gets worse. Eventually, the car would die at speed. The first 3 trips to the dealer, they replaced the PCM (computer), and the fourth time, they fessed up and said that a cam keeps getting stuck and that I'd need a new engine. The trannie was in bad shape, too, after all of the shenanigans.

I'm pretty sure the purchaser was killed on a highway near here 'bout 2 months after I sold it. Pretty sure that was my former car on the TV news.

Cheery news, huh?

Wow, that's disturbing. Thanks for the reply, I'll look into it. Some other symptoms that I should've posted earlier are:
-The speedometer hardly works when the car acts up, and when the speedometer does work, it's all over the place, usually increasing when I accelerate, dropping to zero when I let off the gas.
-The car tends to act up when I accelerate after making a turn, or one of those huge circles on an on-ramp. My old man thinks it might be the mount, any ideas?
-The car could have been in an accident before I bought it; the hood was repainted (poorly)

Any input is appreciated.