1997 BMW 328 indicator lights that stay on

The air bag lamp is lit for what could be several reasons. The seat belt buckle switch or the belt pre-tensioner pyrotechnics are/have faulted, the battery was not disconnected during a repair attempt, the airbag control module has an internal fault, a gas generator has failed or is disconnected. You get the idea. Scan the fault in the SRS control module and see what it is first, then we can go from there. There are some good proprietary grade hand held scanning devices available. Both of the faults you have will require this scanning to both expose the fault as well as reset the warning lamp after the successful completion of the repairs. The "service engine" light is on for what could be something as simple as a loose or missing fuel cap, again the scanning tool will allow the fault to be revealed from the memory(isn't ODBII great!)