Congratulations. You have a really good engine in the M50 which, with a little care and regular maintenance should last a very long time.
A couple of comments if I may;
As noted by others already, regular oil changes are a must. Many people let the service lights tell them when to do it and others do it on mileage. Whichever you choose, use a goo synthetic oil such as Mobil 1. And always replace the filter.
I suspect that any cooling problems may have been casued by the dreaded water pump. They are cheap enough, so my suggestion is to replace it with one that has metal impellers. Always use BMW coolant. No discussion on this one.
As for the transmission Ih am not convinced yours is a sealed for lifetime unit. This was the practice for 530 and 540 models but the 525's got either a four speed unit or a five speed unit. Don't just accpet an opinion on this. Check with the dealer or check your owner's manual. If yours is a sealed unit it is designed to operate for a specific period. It does not have standard ATF and cannot be easily changed on a regular basis. What you can do is have the entire transmission flushed and the old lifetime ATF replaced with new lifetime ATF. Be warned, this is expensive but is a worthwhile way to ensure longer life.
If it is a standard 4 speed unit then your'e laughing as it does take regular ATF and can be easily changed. If you have the adaptive 5 speed box then you can change the ATF but it needs to be done by a professional as it is very sensitive to temperature and volume. Not an easy do it yourself job.
Given that it had a change I would suggest it is the four speed unit. In that case the person who advised you that it contained lifetime ATF was incorrect.
If you don't already own one, get a Bentley's. Follow the maintenance plan to the letter and you should have a really solid and dependable car.
Consider replacing all the ball joints in the front suspension in the near future which will sharpen up the handling and steering like you wouldn't believe.
Hope this info helped.
Geoff
Sydney, Australia
'94 525iA