I guess it all depends on the floor joists and subfloor. The stuff did wonders for me, not a grout line crack, let alone a broken tile in a kitchen/dining, 2 baths and an entry area. Lots of screws, fiber tape and thinset joints. Good luck my man!

Can you handle the extra height of a layer of 1/4 durock concrete board in that room?

Depends on how many lights are on that breaker and the size of wire feeding it. If there is still capacity on that circuit (15 A are the norm with 14G wire). Use 14 from the switch box to the new 15 A outlet box if that is what is feeding the light circuit. Wire up your new ground fault/arc fault as required depending on the basement room. Also make sure you get the correct black wire in the switch box that is line and not switched. Makes sure you tie the new ground wire and white wire to the existing wires in the switch box. Watch some youtube if you get stuck.

Find the leak, water and gravity are very unforgiving.

I like the thread cutting oil from the plumbing department for most stuff, but magic tap cutting fluid is awesome for the tough jobs.