Tire flatspotting is not much of a problem with modern tires. In any case it is a temporary effect. It is most noticable on nylon cord tires which are typically not sold much any more.
If a tire flat spots you only need to drive the car at moderate speeds for a few miles to warm the tire up and the flat spot will go away of its own accord.
Label this one as a minor nusince issue. I am also not that fond of putting a car on jack stands for a couple of reasons. It hangs the suspension components on the bushings in un-natural ways. I've parked many cars for time spans of years with no problem.
The second issue for putting a car on jack stands is if you need to move it in a hurry ( house is on fire, flooding etc. you can't!) Judge your own risk on this issue based on location and conditions where you are storing the car.
I usually inflate the tires to about +5 - +8 psi over normal pressure to be sure the bead stays seated if they develop a slow leak.
Infestation by rodents is greatly increased if the car is parked where tall grass or weeds might provide access ladders up into the engine compartment that otherwise would be very difficult for the rodents.
Racers frequently block tail pipes / headers by finding the appropriate diameter rubber ball, drilling a hole in it and threading a length of rope throught he hole and tieing a knot.
On the pre-storage oil change, and addition of fuel stabilizer, do it a couple days before the car is stored, so the new oil gets pumped through the engine a bit. Lots of anti-corrosion additives don't do you any good setting in the oil pan you want to get them coated onto the parts that are most likely to have most of the oil drain off. Likewise the fuel stabilizer needs to mix and get into the full fuel system.
Also good idea to leave a note on the dash board or drivers seat telling the things that must be done to restart the car, such as reconnect the battery, unplug the tail pipe, remove aluminum foil cover over airfilter or what ever.
They now make small solar battery trickle chargers which help keep a battery alive. If a battery is discharged it is subject to freeze damage so it is useful to keep it on some sort of charging cycle. (even a once every month trickle charge is very helpful). Lead acid batteries can live for 10-15 years if kept fully charged with a low current trickle charger that does not cook the water out of them. The battery does no need to end up damaged or dead. If you let it fully discharge due to its normal slow loss of charge, due to both chemical processes and low current loads like the clock and such that always draw very small amounts of current, it will kill the battery due to sulfation. It is the long term discharge that kills the battery, rather than the battery is discharged because it is dead.
Also make sure dome lights etc. are shut off, as folks have a tendency to bump switches and leave car doors ajar on stored cars. Removing the bulb in the dome light works to prevent it being left on by accident when someone gets in the car to look for that spare snow scraper, or gets in the glove box and does not fully close it if it is one that has a light.
As far as the clutch siezing to the flywheel I have never seen or heard of that happening, and would not think it a good idea to keep the hydraulic clutch system under constanstant pressure holding the clutch off the flywheel and pressure plate.