That is correct.

You seat is pretty much shot.

You cannot repair it to look good. The best you can do is get a heavy cloth patch of a similar color, cut the patch so that it is larger than the torn area and insert the patch into the hole. Apply flexible fabric glue to the patch where it is under the seat coving, place a sheet of wax paper and then a weight on the patch for several hours.

It will look like an obvious patch, but it probably is better than the open hole

That cut probably was made with a single, shaped milling head.

If I was to duplicate, I would use a router.

Cut the slot to match with a straight bit of the right width. Can also be cut on a table saw with care. Then I would put the radius on the sides of the slot with a rounding over bit (the term I know). It appears that the two edges have different radius corners, but that just may be the photo.

Easier said than done.

Make sure that you shut off the main water valve.

Thank you for the link.

That is the best possibility yet.

The one and only question to ask is why would Vikings try to establish a settlement 1000 miles from open waters (Gulf of Mexico) and several thousand more from the nearest Viking settlement.

That is a wide gap without any studs. The suggestions of spanning it with lumber are the best option.

You will have to cut bevels on the back side of the lumber to get a good fit. The bevel doesn't have to be exact, paintable caulk will suffice.

My first thought also was a leaking drain pipe because of the limited range of the damage. A leaking water line would result in visible water, but the intermittent demand on a drain pipe would generate much less leakage. It also appears that the damage is where studs are. Almost certainly the damage shown in the photos showing the outlet is on a stud.

A roof leak is a slight possibility, but if it is a roof leak damage would also appear on the second floor.

My experience is the same. I would occasionally have a small quantity of water in my basement after heavy rains. The house has flower beds and shrubs around the entire perimeter so I piled mulch 6" high around the entire foundation, tapering out about 18" from the foundation. Since then, not a single drop has entered the house. I do add a little more mulch every year to offset settling and composting.

I advise against trying to pry up the tiles for later reuse. Tiles can be removed successfully if you know what you are doing, but it is a real skill and the price for not possessing that skill is permanent.