Hello mate my missus has a T plate E46 318i

Few probs
1st no number plate lights
2nd sometimes when I try to start it it just clicks and the head lights come on full wierd eh I can bump it and it will start but the indicators on the dash don't work but do outside. If I turn it off and restart it they work fine
3rd sometimes when we switch it off and pull the key out the oil light stays on the dash and the heaters keep blowing

The battery is fine as is the connections the starter is good as well so any ideas I was thinking the body control module