Key fob, radio and dome light problems

[Rev1L]

I've got a 2007 Aura XR with around 95,000 miles on it. I'm having a series of issues and I'm curious if they are related.

Key fobs - will work for the trunk and alarm but not to lock/unlock doors or remote start the system. Previous owner said the first time they tried to remote start it worked but caused radio issues.

Radio - sometimes buttons won't work, sometimes they do. Usually it's the menu buttons, right now the load & eject buttons for the 6 disc CD player don't. Radio screen also occasionally becomes very odd. Sometimes randomly pulses, sometimes lights up in a small shape, sometimes other.

Dome light - not turning on automatically when I open any door. I can't find a control for it and the manual indicates it's always completely automatic.

Also the lights on the 2 switches for the 2 front windows aren't lighting up.

Anyone have any ideas or experiences with these issues?