E36 318ti misfire issue

I just "inherited" a 1996 318ti California from my college-age niece. It was towed to my house with the #2 plug blown out. It was also very low on coolant, oil, and power steering fluid. The threads in the head did not look damaged (surprisingly) so I tried putting a new plug in and was able to torque it without any problem. I went ahead and replaced all 4 plugs. I also checked the CR codes (0300, 0302, and 0304).

The engine will start and run fine. However, after running on the freeway for 15-20 minutes, if I pull off and then accelerate sharply (run the rpm up to ~5000 rpm) the check engine light will flash 4 times and then stay on. The motor then runs very roughly (basically runs on 3 cylinders) for the duration. The next day, it will run fine again, CE code show 0302. I did check that the plug is still tight in the head, and that both ends of the wire are secure & tight. The wires themselves are very oil soaked as there are bad oil leaks (the oil filter mount is a obvious large one).

One other odd thing that may or may not be relevant. Before its starting to misfire, while driving on the highway, it beeps twice. Just a quick "beep,beep", no warning lights or other issues. Any idea what that might be?

I don't want to spend much money on this thing until I have a better idea of what may be involved. It needs a lot of other stuff like shocks/struts, interior work, tires, etc. Looking for suggestions of what to look at/try next. Plug wires? Have the coil pack tested (no idea how to test myself since it obviously sparks when I start the car)?

Thanks.

Before you install new parts on trial and error basis, I would once drive to the dealer for a real fault code analysis with the computer system. Let them explain all the faults, drive home, buy a Bentley Repair Manual for the E36 and start repairing it DIY and buy the parts from the usual online shops.

What does error code P0302 for the check engine light mean?
P0302 means number two cylinder has a misfire,
What does error code P0302 for the check engine light mean

Causes
A code P0302 may mean that one or more of the following has happened:

Faulty spark plug or wire
Faulty coil (pack)
Faulty oxygen sensor(s)
Faulty fuel injector
Burned exhaust valve
Faulty catalytic converter(s)
Running out of fuel
Poor compression
Defective computer

If there are symptoms such as the engine is stumbling or hesitating, check all wiring and connectors that lead to the cylinders (i.e. spark plugs). Depending on how long the ignition components have been in the car, it may be a good idea to replace them as part of your regular maintenance schedule. I would suggest spark plugs, spark plug wires, distributor cap, and rotor (if applicable). Otherwise, check the coils (a.k.a. coil packs). In some cases, the catalytic converter has gone bad. There are also cases that the problems were faulty fuel injectors.

Thanks for the reply. I already knew what the codes meant, was really looking for some input on which direction to look (electrical? injectors? etc.). I was able to move some of the spark plug wires around and the code followed the one wire so I will probably try a wire set first. Taking the car to a dealer is fairly inconvenient but I guess I may end up going down that road at some point. Will definitely look at a Bently manual. Car came with a Haynes and an electronic manual that my PC does not like, still trying to get that to work.

Oil soaked plug wires will break down. 1)Fix leaks; 2) Replace plug wires. See how it goes then and make further decisions.