If you mean for a swim practice then yes... If you mean in a local pool then yes... If you mean in meets or compititions then no.
Yes, men can wear socks while swimming in their pool. Most people prefer not to wear socks, but to each his own.
Preferably a swimsuit.
Many swimmers (in a pool) wear swimming goggles.
wear a bunch of heavy stuff
Yes.
Modesty in public. Once at the pool disrobe. When ready to leave don clothes again.
wedding ring
swimming trunks
Because Muslims are not allowed to wear jewelry during Ramadan.
Yes Yes
that black discoloration is known as tarnish, or corrosion. A recommendation would be to not wear jewelry while swimming. The reason all of this is happening is because of the chlorine. Chlorine reacts to silver VERY quickly and will eat the metal away. You have two choices, remove the chlorine (unwise) convert to salt water, or NOT wear silver clad things in the pool
Swimming in a pool with chlorine while on your period is generally safe and shouldn't cause any issues. The chlorine in the pool will kill off most bacteria, and any menstrual blood will be diluted in the pool water. It's important to wear tampons or menstrual cups while swimming to prevent leakage.