Is this washer supposed to be free floating or in the housing?! Thanks in advance!!

That washer goes directly under the nut, on the outside (front) of the propeller.

Not sure I follow your instructions... Do you leave it outside the housing or jam it inside that deal to prevent moisture from getting in there??

The part you are actually touching with the pliers in the photo is a seal, the other part that looks like a washer is just that, a washer to hold in the seal. The seal itself should be inside the housing, and that washer should be flush with the housing, not down inside of it. as long as the seal is down inside the opening in the housing, water can't get in. There is another washer, the one I was referring to before, that goes directly under the prop nut.

You should be able to press the seal down into the housing by tightening down the nut on the propeller (gently). Put some grease on the seal first. If it doesn't fit, there may be a small nick or burr on the seal or in the housing which you can address by lightly sanding it. If the entire seal won't sit in the housing, you can buy a new housing and seal on line, rather inexpensively. The housing is easily replaceable by the two screws visible in your photo.

That seal is the part that is damaged by fishing line, causing leaks and damage to the shaft and armature. Not a bad idea to have one available for future use anyway in case line gets into it.

Coat the shaft, seal, washers, nut etc. with good quality marine grease when reassembling it.

The seal in the pic needs to be pushed down in the end cap. Tightening the bolt will not seat it down, no matter how much you tighten it. It needs to be pushed down as far as possible (should have between 1/8 and 1/4 inch of space). Take the 2 bolts out, pull the cap, and press the seal back in.

Don't have to remove the cap to reseat seal. Can use a deep socket and put over the prop shaft, then tap the seal back into place.
John