You can move the cig lighter wire to another wire on your fuse panel. my lighter doesn't work either. I'm lazy. I dont know if our car's lighter is hot with key or hot all the time. I would do the latter so toys/phone can charge when you're away.
my dome light flickers a lot. mine i know is a crappy passenger door switch, because i can select it to ON. However it does flicker when i select between the three modes, so its a matter of time before it fails. Take it out and look for corrosion.
if your car is pre 96 the previous owner may have removed bulbs to scoot by an inspection test. to pull your cluster out is a 10 minute job...5 mins finding the tools. If you have small hands and tough skin you can probably cut another minute off. Once the cluster is out you can also do some probing with a multimeter.