Hi Dan
There are 2 relays to check/change one is the Fuel Pump Relay the second is the Power Relay
Lights, you say you have changed to BMW angel eyes, did you change the complete headlamp unit? Just changing the bulbs to LED may give a bulb failure warning unless they are fitted with a resistor (most are) but wouldn't have an effect on the FRM. The FRM is a control unit not a power supply it controls many systems and acts as a confirmation gateway for others. Getting it working will eliminate a few more faults, often fault codes cant be reset while there is a fault in an associated unit.
As you have a non starting car I would pull the FRM, contact one of the repairers and send it off for checking and repair. If you can stick with the original you avoid all the re-programming issues. If it cant be repaired then a replacement will be needed, BMW and some Specialists will tell you that "Only BMW can program a unit" Well they would I suppose. They are wrong and you already have the kit to do it (just another School day)
Dave