Correct English would use had been since it is an indirect speech case
Not sure what you are referring to. The translation above is using HAD BEEN
Maybe the Duolingo accepted "has already been" ? Is it tolerable?
It is accepted. Others have to decide how good or bad it is.
Why is it "ses" here?
dozvědět uses the reflexive : už jsi se = už ses
jak jsi se = jak ses
Why is "byl už třikrat ženaty" wrong?
"Kateřino, jak ses dozvěděla, že byl už třikrát ženatý?" - It's definitely right.
"Kateřina, how did you learn that he was already married three times?" (Reported) Sorry, but I need to know if this is really a bad use of the past tense. I still have a little mess in that.
"Kateřino, jak ses dozvěděla, že už byl třikrát ženatý?" Is that the same translatin for how did you find out...?
Yes, we use "jak ses (jsi se) dozvěděla (dozvěděl)..." or "jak jsi zjistila (zjistil)..." for "how did you find out..." and also for "how did you learn..."