Wall plate and subfloor repair in bathroom
Firstly, protect your bathtub. Scratches don't heal, and repairs aren't easy or cheap. Tape cardboard or heavy paper over the face and top surfaces, then lay blankets or towels over that.
Secondly, the wall plate doesn't necessarily need replacement. After your floor repair is complete, replace that short block with a fresh one. That'll provide adequate backing for drywall. There are no structural concerns with such a small area of damage.
Regarding the floor repair, I can't be too specific until we see what's under there, but the process looks like this:

Cut out the subfloor with whatever tools you have on hand. A circular saw set to depth, a reciprocating saw, and a sharp chisel can all be effective. Be careful not to damage the joists or any utility hardware below. Cuts should go no deeper than about 1/8&quot; into the framing. Use a square to make right angles so that your patches are rectangular. This makes fitting a new piece easier.
Where your patch edges don't land on joists, add two-by blocking. This can be one of two things: Blocks sistered onto or spanning between joists; blocks floated under the edge of the remaining subfloor. They should be securely screwed to other framing where possible.
Place the subfloor patch, screwing it to all available backing. All edges should be supported.

At all points of contact, use 2-1/2&quot; or 3&quot; gold construction screws (not drywall screws, which are brittle), and construction adhesive, which bolsters connections and eliminates most noise. Don't rely on just adhesive for any connection, though.