Mostly, everything is possible. It just boils down to cost.
It may cost more to modify something to suit another purpose.
There will me more work to cut the grille (sliding) to suit the size of the swing grill door. Both dimensions are different.
As for cutting the existing plywood flush door to insert a glass, it will involve the removal of the plywood which will be damaged.

Basically, all will be cheaper if you get then new, to your specifications. Looks better as well.

I believe you are referring to your bathroom door frame. If the damage is less than 6" from the floor, then can repair using cement sand. This will also depend on your expectation.

This method has been used in the construction more than 30 years ago. They basically protect the timber frame from damaged due to water. This practice is not use in construction nowadays.
The outcome is OK if done nicely. Once painted, will not be noticeable.
PMed you the method