First, please fill out your info
<--------here so we know what type of vehicle you're working with. There are different systems in the engine depending on year and other good stuff.
Wiper motor is probably going bad (mine is, I just don't ever use my rear wiper, oh well) headlights and VIC (your center screen) are most likely bad solder joints, and just need to be redone. Or rip out the VIC all together. Might need a new headlight switch? Do the headlights work fine when you switch them into the on position (as in no flicker with the switch in this position).
Oil pressure should adjust depending on rpms, approx 10 per 1000rpms. Get your battery and alternator tested (many auto part stores will do this for free), always a good place to start. Depending on how well your family maintains the vehicle, it might be worth just doing a good tune up and cleaning.
His:00 TJ "Fiona" stuff/stuff/stuff
95 ZJ 3.5" w/242 swap-Sold
Hers: 15 JK Sahara-3" Teraflex