Dave -
Let me try to answer as many questions as I can for you:
First, if suds are coming up the agitator, that's a sign that water is rising up the centerpost, which is to be expected of machines of this era, actually of any worn belt-drive washer. The full-size centerpost models that were made up until 1978 are generally immune from flooding centerposts due to height of the post, but if water levels are frequently run too high, or as we AW.org members sometimes like to raise the water level, the post can still get flooded. To correct this, the agitator shaft and spin-tube seals need to be replaced. If you have bearings going bad, the spin tube seal will be replaced anyway during that job.
"The spin is a little noisy" - this is COMMON on early to 1977 belt-drive machines and is a sign of bearing wear, not necessarily from wet bearings, though water might exascerbate the problem. To fully correct this, new bearings and a new spin tube are in order.
The agitator not spinning freely with the basket is a sign that lubrication has fallen down onto the Tee-bearing that supports the spin tube. This happens as centerpost seals fail, OR it could have been put in that way after the machine was serviced. The agitator should turn exactly with the basket. The Vari-Flex agitators are heavy - if any agitator is going to get dragged down and not spin freely, it would be this one.
Water leaking onto the motor is usually a sign of a leaking tub or tub centerpost gasket, OR the airdome. You will seldom hear me make a derrogatory comment about Whirlpool, but why they put the airdome directly above the motor is beyond me. I know it needed to fit in a cabinet corner, but there are four of them!! The airdome is what controls air pressure to the level switch.
That disk thing IS a lint filter, and if you have a flat, flying saucer looking one, it's a replacement. The original was a cone or funnel shaped filter that seemed to either crack easily or get clogged, and this disk design is a long-ago designed service and production replacement which was used until the tub-mounted filters came about in the mid-70s. It could be leaking, especially if it has ever frozen as it usually always contains water unless the machine has been allowed (for years) to dry fully. Dolly carts and unscrupulous movers have been known to disturb these filters.
Do you hear the sounds of any of the dispenser solenoids working? Yours probably does not work due to clogs either in the supply hose from the pump, an innop. valve which is under the transmission, OR due to hoses at the dispenser being clogged. VERY CAREFULLY remove the dispenser from the machine for cleaning. There is brittle plastic there that gets more brittle with age and exposure to bleach and detergents. That is a $100 dispenser if you have to replace it.
The control panel light could be the switch (do you hear it click when you open the door?), the bulb, or the starter. Just start taking screws off the panel itself and see what you get - I don't remember exactly the configuration of mine to say how it came apart but it wasn't a challenge. Are you certain there is a bulb installed?
The front corner gusset of the machine being missing may present a challenge. These are not made anymore and they were welded onto the cabinet. Not sure what to tell you there, but look for leaks above that area that may have rusted the gusset out. The tear in the cabinet would not scare me, however these tend to make the cabinets wobbly and less supportive when moving machines. I had a 1982 machine back in the 90s that had a six-inch tear above the rear leg. I got some brackets from Home-Depot, drilled them onto the inside of the cabinet like a butterfly bandage, and it held well, though those damn screws were sharp if I ever reached inside after that.
Pulling the agitator is easy - pop the round shiny cap off with a flat blade screw driver. This should reveal a bolt that you can turn counter clockwise (while holding the agitator). Once the bolt is out, if the agitator is not rusted onto the splines, it should lift out with some force. Pull up from the skirt and with a variflex, you'll put the 'tator apart if you dont.
Once the agitator is out, you can take the basket out but you'll need a spanner wrench and a good hammer to do it. Check Robert's Lady K restoration pics - this procedure is well documented in there and it covers darn near every washer Whirlpool has ever made (DDs are even constructed the same way and use the same parts).
Pulling the top up is easy - put your fingers inside the lid well. Pull yourself up and out (in a northwest direction) and it should come right up.
Replacing the bearings and the spin tube may present a few challenges, and we'll go into that in greater detail when you get that far. The spin tube is an easy change, but you need either a very special basket drive assembly with the narrow-belt pulley, or you have to rebuild your current one with a new tube.
You have a lot of work cut-out for you on this machine, BUT, everything you do will more or less one-for-one transfer to the electronic set, so you'll be doing yourself learning-curve benefits.
GOOD LUCK!
Gordon