New gal from UT here! Need some help.
What safety related things would you recommend I check out with it?
Here's what I would do if the car were mine. First, get a Factory Service Manual for it. You can download one here:
Service Manuals – MyMopar. I have the downloads for my cars, but I prefer a printed FSM so I get them from Faxon Auto Literature. They put out a nice product. I use their reprints as they are clean and new but they often have an old original one if you want it and don't mind the higher cost.
Sort of in order by importance to check are:
Tires - check for tread condition and wear, but also check the date codes. Opinions vary, but I get uncomfortable when a tire's more than 10 years old. Old tires used just to putt around town at low speeds while sorting out what you have is less of a concern than out on the highway. Old tires can come unglued with no warning.
Brakes - pull the wheels and check for leaks. Trace the brake lines back to the master cylinder and check the connections for leaks, and also at the wheel cylinders. See if the linings are in a serviceable range. Make sure they are adjusted properly. If driving and braking with very gentle touch on the steering wheel, does it stop in a straight line or pull to one side? When you check the front brakes and pull the hub, look at the bearings. This is a good time to repack them if needed.
Steering - Is the steering sloppy or loose? Look at all the fittings under the car. Are the rubber boots in good shape (not torn or cracked)? If you sit in it with the engine off, does the wheel turn a lot before you meet resistance from the tires starting to turn? Does it drive in a straight line with again a gentle touch on the wheel?
Electrical - This has been addressed, but yes it's a good idea to sort this out promptly. In addition to your wonky flickering issue I'd go through and turn on everything to make sure all items are working properly.
Fluids - Check everywhere for leaks. Change all the fluids and filters. Oil, radiator, power steering if you have it, transmission, and rear end. Backflush the radiator.
Belts and hoses - Check for condition and wear. When belts get old they look "shiny" on the inside and/or start to show cracks. Hoses should be pliable (not stiff and hard) when squeezed. Unless they are clearly new I replace all of these and save the old ones for spares in the trunk should I need one while out and about.
Tune-up - I don't see any electronic ignition stuff so I'm assuming you have a points car. Do a basic tune-up and replace the cap, rotor, points, condenser, and plugs. If the wires are old, stiff, or cracked replace them too.
@halifaxhops is a quality member here who sells the good stuff (not Chinese junk) for a tune-up.
Heater - Look for leaks anywhere and especially inside the car. If none, start with checking the fuse. If that's good check your fan switch, and if that's good check the blower motor. One of them will be most likely be faulty and the reason it doesn't work.
A/C - You'll have to get help on this one from other members, I don't have A/C on anything and can't help here.
I saw you just filled your gas tank, get some Sta-Bil from the parts store and treat the gas. That will help it last quite a while.
Above all, don't be shy. You don't need to already know how to work on your car to get this done. The gurus will walk you through diagnosing and fixing one step at a time. When going down the diagnose-and-fix trail make sure to take lots of good clear pictures for those trying to help you. Good luck on your voyage, I'm jealous of your car - it's a beauty!