The black hands you describe are nuptial pads male frogs get and they're used for mating so they can more easily grasp a female. It seems to come and go randomly, some days on my male frog it's noticeable other days not so much.

Since you have three males but only one female you may want to keep an eye on them to make sure they don't get too frisky on your female, a 3:1 ratio could possibly stress her out. Having plants or caves so the female could get a break from the males may help, if frisky business did start to occur.

Then again my male frog gets 'dirty man hands' a lot but he doesn't sing and I've never seen him put the moves on my other frogs. I hear that these frogs do not mate often in home aquariums and to get them to breed in laboratories they are exposed to certain chemicals, then again other things could triggering mating too (like adding fresh, cool water which simulates fresh rainfall).

Probably nothing to worry about but I would keep an eye on it.

I thought my male frog was going to be female too, the guy is huge and as large as my female. I still have no idea what sex my third frog is, he's small but no nuptial pads and he's a bit of a chub.