It’s just a pointless counter for the time being. It may do something in the future, it might not.
And no, I think only Jessica can do buttsecks. Not counting a handful of side girls.
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The things in parenthesis? Like (Auntie) for Jessica?
Those are quirks. Certain events turn them on, for the moment they’re just some sort of “achievement”.
It is planned to have them unlock certain scenes.
Like the (Adultress) quirk will unlock scenes like the one it’s unlocked.
If you meant the text that appears next to the stats. That’s just flavour text, it changes every couple of levels up to 20.