Re-assembly tips

Are you dealing with a 2-stroke or a 4-stroke engine?
While most re-assembly techniques are the same, the devil is in the details and you want to detail it correctly per what type of engine it is.

Ok then.
First, you will need a complete gasket kit, either home made from quality gasket material or bought from a vendor.
I recommend using the upgraded exhaust gasket from SBP.

I never EVER recommend using gasoline as a cleaning fluid. It is waaaaay too flammable to risk using.
No matter what you use though, having a fire extinguisher close by is a must.
Also, get yourself some solvent resistant rubber gloves. They are usually quite thick and either blue or black in color. Be sure to read the label to be sure that they are in fact solvent resistant. Plain old dish washing gloves are not up to the task and will turn to goo. Safety glasses or goggles are a must as well!
I recommend using mineral spirits as a cleaning fluid. I use a paint roller tray as a basin and a paint brush with the bristles cut short for the tool. Pipe cleaners work very well for cleaning the inside of the holes and cleaning out the threaded blind holes.
Every part needs to be absolutely dry and dust free before assembling.
The assembly area needs to be very clean and dust free. A table in the back yard is not a good place to do this at.
The crank bearings should be lubricated with a drop or two of pre-mix oil.
The transmission bearings should be greased with a high temp grease.
I prefer the high temp red grease "suitable for use with European cars" for all grease applications.
Place a good sized blob of grease in the palm of one hand and with the other hand scrape the bearing against the greasy hand and through the grease blob. Keep doing this until the grease has been worked through the bearing and out the other side. Your hands should be a sticky, greasy mess if you are doing it right.
The clutch spring assembly needs to be packed with grease.
The release ball and bar need thorough greasing as well as the hollow shaft.
The reduction gears need a wafer thin coat of grease on all the teeth. A toothbrush works well for spreading the grease around.

When installing a bearing into a hole only apply pressure to the outside race of the bearing.
When installing a bearing onto a shaft, only apply pressure to the inside race of the bearing. The idea here is while installing to not load the bearing through the actual bearing balls or else you will leave deformations in the races which will cause early failure as the balls will no longer have a smooth race to roll around in.
Oil or grease the outside of a bearing and the hole it will be installed into.
Oil or grease the inside of a bearing and the shaft it will be installed onto.
The same goes for seals. Never install a bearing or seal dry.
A gasket dressing such as Hylomar is highly recommended for the crank case gasket as well as all the other gaskets. Hylomar is easiest to apply with a q-tip dipped in acetone to spread it around. Coat both sides of the gasket. Wax paper makes for a good surface to lay the coated side of a gasket onto when coating the other side. Let it set up until it is tacky and install.

The hardware should be tightened in a cris-cross pattern as if you were drawing a picture of a star. This is to prevent warping of the cases.
Blue loc-tite is good to use on the threads of all fasteners.
Start with 24inlb, go around all the fasteners, then go to 72inlb, go around all the fasteners, then go to 96 inlb and final torque all the fasteners. Check final torque twice, still keeping the star pattern as you go along. It needs to be done this way to insure that the cases are evenly drawn together and once again, no warping occurs.

This is just the beginning of a good re-assembly job.
Feel free to ask questions if you have any.

Pre-mix oil is in fact the oil you mix with the gasoline prior to pouring the fuel into your gas tank. You got that one correct.

There is no oil slinger in these engines. They have no use for one.

The little shims are very important. They are what hold the flywheels in proper location in regards to the flywheels shifting left or right inside the crank cases. Without them the flywheels are free to move sideways at will and that will cause alot of damage to the engine. If you only found 1/2 of a shim, then I bet you are correct in your evaluation. You just found what let go internally and ruined the top end.
You really should not be missing one upon re-assembly. If there is a motorcycle parts store near your place, check them out to see if they have a shim of a similar size. There has to be a transmission shim out there that will come close enough to work for you. The inside diameter hole size as well as the thickness are most important to match up.
If push comes to shove, I do not recommend using a steel washer as they are made of low carbon steel and not high carbon tempered steel like a shim is. It will not wear very well and can fail early on.

Crank bearings are the ball bearings on the left and right crankshafts.
Usually there will be a shim set between the outer face of the flywheels and each flywheel bearing. Occasionally there is only one shim set on one side of the flywheels and none on the other side. It all depends on how the flywheels need shimming to center them inside the crank cases. Shims never go on the outside of the bearings, unless they are there to space out something such as the magneto rotor, ect.

Connecting rod bearings are the bearings located on either end of the connecting rod. The "big end" bearing is located where the connecting rod attaches to the flywheels, onto the crank pin. (The crank pin is the shaft that connects the 2 flywheel halves together) The "small end" bearing is located where the connecting rod attaches to the piston, onto the wrist pin (also known as a piston pin).

The connecting rod bearings should be lubricated lightly with pre-mix oil.

As far as any bearings associated with the flywheels of a 2-stroke engine, never ever under any circumstances use axle grease as an assembly lube. It will not wash off or blend in with the fuel oil as the engine is ran and that will lead to premature bearing failure as the grease looses it's lubricity. It is a common idea that axle grease will melt away in the presence of engine oil. That is not true. In fact, the use of axle grease will prevent engine oil from ever getting into the bearings properly.

Assembly lube, of which some types are similar to a grease, can be used. It will melt or blend in with engine oil and/ or pre-mix oil as the engine is ran.

The transmission bearings are the bearings located on either end of the transmission shaft. One is on the clutch end, the other is on the drive sprocket end. These can be lubricated with axle grease.

The teeny tiny bearings inside the clutch hub should be lubricated with white lithium grease, very, very sparingly applied. Too much of it there and it will fling out due to centrifugal force and contaminate the clutch friction pads. One should really never try to disassemble the clutch hub though. If you look on the backside of the clutch you will see 3 small holes where the white lithium grease can be applied through. Alternatively, with the outer clutch disc removed, you usually can push the clutch outer ring gear to one side on the clutch hub and open up a slight gap between the two and get the white lithium grease in there that way.

Bearings are more easily messed up than most folks realize. Any severe side loading such as banging with a hammer or prying away on one to get it off of a shaft or out of a hole in a manner that is done wrong will ruin a bearing. As stated before, if you are pulling a bearing off of or pressing a bearing onto a shaft, only apply pressure to the inside race. If you are pulling a bearing out of or pressing a bearing into a hole, only apply pressure to the outside race.

One other thing, use pre-mix oil as an assembly lube when installing the piston into the cylinder, and be double sure that the gaps between the piston rings are centered over the locating dowels in the piston.

Wish I would have read this earlier today...did not use any pre-mix oil when installing the piston into the cylinder head. Guess I tear it all back down tomorrow and start over.

Are there any torque specs for the transmission nut, the magneto nut, or the "little sprocket (output)" nut? Don't mean to hijack, but I think this is a perfect thread for the info.

While oiling the cylinder and piston during assembly is the correct way to do it, now that you have it all back together I would put about 2 tablespoons of pre-mix oil down the spark plug hole and crank the engine over to coat the cylinder. Not correct, but marginally adequate.
As for the torques on the transmission nuts, I have not seen any. Tight is tight on those, but don't over do it. if I had to guess, I would say 10 to 15 ftlb should be fine.