I would leave engine alone until it starts to show signs of problems, compression sounds good if motor still climbs the hills, timing belt needs to be replace every 100k or so, O2 sensor(front one) as well, but you will see slight drop in MPG at that time.
No on synthetic oil, high mile oil is fine to use.
Shifter moving means motor mount or trans mount is loose or broken.
Open hood, Set parking brake, then start engine
Put in 1st then slowly let out the clutch while watching engine, you are look for lifting of one side, loose or broken motor mount
Now do the same but in Reverse, watch for movement the other way.
If it seems tight then trans mount is probably the issue.
Ranger hydraulic clutch system is marginal at best, no room for even a little air in the system.
You can rebleed the system, and put in fresh brake fluid(that is what is used).
Make sure reservoir is topped up.
Next time a new clutch is needed replace Master along with slave.
This is why it can be hard to get it into 1st when stopped with engine running.
Clean the IAC(idle air control) Valve, not hard to do, it could be sticking so idle drops to low when stopping.
This could mean pilot bearing in clutch setup is broken,(also why it is hard to shift into 1st when stopped), pilot bearing allows engine/flywheel to spin at a different RPM than the transmission input shaft.
When trans is in gear the input shaft is connected to the rear wheels, the clutch separates flywheel and input shaft but only if pilot bearing is working well.
When in Neutral the input shaft is disconnected from the rear wheels.
So try this, shift into Neutral when coming to a stop don't leave trans in gear with clutch pedal in, and then see if it still stalls.
If it doesn't then yes could be pilot bearing issue, its a long shot though.
ABS and airbag have lots of possible issues.
Have a read here first: 1997 Ford Ranger: OFF...airbag light..ABS light..the air bag
Could just be a fuse, or two