Should I fix the swimming pool with plaster or a clorinated rubber

What I have done on my 1909 house (I am in the U.S.) in the same exact situation is clear a wider area of the lath and plaster and replace it with drywall. To do that, you will need to add some padding over the studs because the lath&plaster is thicker than 1/2" -- what I did was pad it with 3/8" plywood, then drywall over plywood to achieve approximately an even joint between the new drywall and the old plaster. Then you tape and sand the joints like you would with regular drywall, prime and paint it later.

Yes, you should remove the trim before the ceiling is done.

Yes, some and possibly a lot of the material will get damaged if you have not done it before. Even a pro will crack some, but a pro will know how to repair it too. Sometimes it is better to get a new molding that closely matches the original.

Yes, the wall will get damaged too here and there but the same crew doing the plaster can mud in the damaged spots too.