Toss the piston. It was probably straight gassed.
Some things to check;
Move the connecting rod laterally side to side.....see how much slop it has. Also grab it and force it up and down(crank not moving)...looking for slop there too.
Grab the crank ends on ea side, one at a time and see if there is any lateral play in the crank itself(you'll have to remove the flywheel). Clutch side most likely to have play.
You can remove the flywheel with the puller screw holes. You can either buy a chainsaw flywheel remover tool or makeshift a steering wheel puller to do the task. One caveat there is to only thread the puller screws the thickness of the flywheel.....anymore and you can do damage underneath the flywheel.
Replace all gas & vent tubing
In answer to some of your questions;
50/50 acetone & ATF makes a great rust break solvent....don't waste your money on store bought stuff. WD-40 is a water displacement formula that is the most overrated substance in the world. But it's gentle on paint and would probably loosen minor pitch and sawdust gunk. Brake cleaner works better, but chase it with something like water from a spray bottle so that it doesn't take off your paint.
Lubriplate is excellent to coat moving parts going back together. But in chainsaws, you can use the oil you have for the gas mix...use it straight. Coat the wrist pin, the piston rings...smear some oil in the cylinder itself. Any extra will burn out. There are very inexpensive plastic tools(ring compressor) to put your piston back into the cylinder.....saves you from fumbling around with the ring(s). Pay attention to how the ring position is, in your piston. You can put them in upside down with catastrophic results.
As far as cleaning parts, I use straight non-ethanol gas and a parts brush. Brake cleaner works too. Things like the carb body & parts I put into a USC. I have gal cans of carb cleaner that come with a dip tray. Most of the time, I will use that in the USC with its heater on....NO rubber type parts go in there. Buy authentic Tilly kits if you can. Pay attention to the carb-to-manifold gasket you take off. The full Tilly kit may not have that correct gasket.
Evaporust will probably work fine on the muffler. At least enough to use high heat engine paint if that's what you're after to pretty 'er up.
Lacquer thinner is a great solvent, but it will take off the paint for sure. Be careful with strong solvents and plastic parts.
Drum bearing needs to be greased.
The use of Loctite is up to the user. Fasteners that typically tend to loosen as I use saws get the Blue Loctite. If your muffler bolts don't have a locking plate, you could consider using Loctite 2620....it will take the heat but it will be difficult later to get those bolts out...you'll have to use a torch. I generally don't put any Loctite on my muffler bolts because all but the 2620 will liquefy anyway with the heat. Some models have a problem with muffler bolts staying tight...do the research there or ask here. I'm not sure about your model.
You should make an attempt at cleaning your crank bearings....they often are packed with sawdust. You can do that by repeated rinsing of your case with gas/oil mix. Should consider replacing the crank seals at this time because with them removed, it will be easier to clean out the crank bearings(and see what's going on). Using a compressor at this point will aid you as well.
If you need good visuals, YouTube is loaded with them.....just stay with people that are well-known chainsaw mechanics and not weekend warriors who have found a 'better way'.
If you can find a Workshop Manual for your saw model....get it. The older Jonsered(s) had great Workshop Manuals....the newer Jonsered/Husqvarna manuals, not so much.
It's easier to answer questions if you list them line after line....instead of all in a paragraph....at least for me.
Kevin