Hi Welcome to GTA ownership
1. Not sure TBH it's dark and cold outside at the moment.
2. Mine did that and it was a sidelight, though it was difficult to tell.
3. Suggest you get the battery checked, mine failed shortly after I bought it, I think if the cars stand about a lot at a dealer the alarms flatten the batteries.
4. Can't help mines got the SatNav radio
5. I've always yanked it out, it doesn't seem to be adjustable much.