Need some help with some bizarre symptoms in my truck.
I have a SyncUP monitor plugged into the OBDCII port and about 3 weeks ago it reported P0304, P0305 codes and the check engine light came on briefly on starting but went off again after it idled for a few seconds.
Drove fine for a few days then got the same codes plus P0316. This time the check engine stayed on.

1. Replaced the plugs, wires and ignition coil. Was tough getting at #3 but finished the job.
2. Started the truck, no check engine, and it didn't throw any more codes.
3. Sat in the truck (turned off) with the fellow who helped me, when the horn came on all by itself and wouldn't stop. Disconnected the horn.
4. Weird clicking sounds came out from behind/around the passengers' side fuse box.
5. I drove the truck with no issues for 2 or 3 days. In fact it had way better power and ran real smooth.
6. Came home and parked it in my driveway. That was two days ago.
7. Today, engine tried to turn over but just 'thumped'. On the fourth try it started, but shook real bad and the check engine light came on again. I drove it for about a mile and came home.
8. Same codes, P0304, P0305, P0316 and now P0300.
9. Tried the "tailpipe paper test" and the paper didn't get sucked in.
10. Just got the oil changed about a month ago and the oil looks ok. No choco milkshake color.
11. What to check next??? Hoping its not burnt exhaust valves but The strange electrical stuff has me scratching my head on this too.

FYI - the engine overheated around Christmas, nearly 4 months ago, but these problems are recent.

 

Test battery volts key off
12.3v to 12.8volts is acceptable
12.2v or less is a failing battery or failed alternator

Start engine, test battery voltage engine running
13.5v to 14.8volts is acceptable
Under 13.5v is a failed alternator

A car battery is ONLY there to start the engine
The alternator provides ALL the voltage after start up, and at a higher voltage than the battery so the battery is charged up while driving, so it can re-start the engine the next time

Engine needs Voltage to run, electric fuel pump/injectors/computer and the Spark system
If alternator is not working and battery voltage is low, engine can not run well