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.
wedding ring
Modesty in public. Once at the pool disrobe. When ready to leave don clothes again.
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
I don't know the exact chemical reaction but my wife and I were told by the jewler not to wear our wedding rings in the pool. I took chemistry in college and I'm pretty sure chlorine forms hydrochloric acid in water, so there is a dilute acidic solution in swimming pools. So the reaction involved is between a metal and an acid.