Q1. How necessary is a cleaning machine for an occasional (say, 3x/mo.) vinyl listener with irreplaceable LPs?Not at all. Convenient. Not necessary.
Q2. If needed, which product delivers most bang for the buck?
That said, a vacuum like VPI 16 will speed things up and do a better job compared to by hand.
Q3. Same questions re stylus cleaning devices.What device? I use a brush. Same exact one since the 1970's. Good enough for Stanton, good enough for Koetsu. Good enough for me.
Q4. Same questions re record preservation treatments.
Clean em, play em, carefully blow or brush off the occasional speck of dust.
Q5. Tracking/alignment/pressure have not been checked or adjusted since acquisition despite two moves. Are there still shops performing these services?
Never take your deck to a shop except as a last resort. DIY all the way. Use MoFi Geo-Disk for alignment, your choice of stylus force gauge for VTF. Learn to fine tune VTA. It is just not that hard.
I can just about guarantee this is the least stuff/simplest advice you will get. I can totally guarantee if you hear the results you will be floored. https://systems.audiogon.com/systems/8367 This is just nowhere near as hard as people make it out to be.
One thing you didn't ask, cleaning solution. Matters far more than the machine. Whole bunch of things will give excellent results so long as you wind up with distilled water rinse and vacuum off. Walker Enzyme 4 Step is preferred, but seriously a lot of stuff will work just fine.