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You need to make sure that there is water in the toilet, shower, or in the vanity ptrap. The water in the ptrap prevents the sewer gases from coming out and stinking up the room

You can install a hubless cast iron wye for about $10.

You need to use a two part epoxy like jb weld.

This very easy. Hopefully the sink drain line is in the wall that you plan to drain the wwashing machine. If not, you will have to open the floor. As for the electrical, you can ta into any outlet...

PVC is easy enough to cut and repair. I would pressure the line first. How far does the pipe travel. Just install new pipe if you can't find the leak. 2" pvc pipe is pretty cheap.

You don't have to cut the tile You can get a flange that fits into the abs pipe coming out of the floor. You could also use a speed ring that attatches to the floor and hold th toilet bolts.

Did you have leaking before? Sounds like you need to change the seats. Maybe at one time the washers were totally bad, causing metal to hit metal. Is the leak ho or cold water?

One solution may be that if the standing pipe drain that the washing machine drains into is to short or long , the sewer gas may be entering the room. The standing pipe drain is attached to a ptrap....

Normally water pressure for residential homes should be between 40 and 60 psi. Since you are pumping from a lake, 40 should be fine. You also have to ask yourself is the pressure when taking a shower...