Welcome aboard the board... :)
On the euro e34 I don't think Engine check is used- it is what was used prior (on e23, 24, 28 and so on). e34 has an LCD panel to provide a better description of the problem at hand.
In the US they use it to comply with the regualtions that state that all cars with diagnostics have to display the info so you are not tied to dealer servicing. It was a big problem with Dealers locking customers into using them in such a pre-meditated fashion. Something that we in Oztralia don't give stuff about of course... and in europe would not happen, as workshops organise their equipment and staff in a more long-term fashion as opposed to looking always engineering new ways to scam customers :P
The seatbelt light is a 10 second (or so) warning unless yours has pre-tensioners, etc. in which case it may be smarter about seatbelt status. My car was not messed with before I got it, and my CEL was missing. The seatbelt warning may have been also, or maybe was blown. I can't remember. I have put a bulb in each now, but never seen the CEL come on, even with a recent oil pressure warning!
If you are worried, go over the car. There will be problems if you are right about the PO. Usually these cars have been well looked after, and at this age the level of idiocy in the maintenance is limited to simple things like 'free-flow' exhausts to replace the 'restrictve factory setup', poor leather care, incorrect rear camber (if lowered) and the use of incorrect coolant (can be tragic) and not changing the brake fluid regularly or with using trans, brake and power steering fluid of the correct type.
If you are new to the car, change all fluids for what you know or can verify with other forum members to be correct. Clean her up and make a spreadsheet of the wear items coming up, or required quickly. Planning is the secret to affordable BMW ownership in the long-term.
Keep a log of everything you do also, it helps to know what was done when, its easy to forget. No girlfriend likes that :) Nick