Is Bowser jr the Koopaling's biological brother or is he their half brother.

Tough. Well Super Mario wiki has mentioned that is a mystery, because the website sinabi Bowletta, their mother, never sinabi `Koopalings come her' to Bowser Jr, either Junior doesn't share a mother and he never listens to Bowletta, or his real mother is dead

whos to say that the koopalings werent adopted??? and they are bowser juniors half sibs???dont ask who the mom is.idk

I think (read somewhere) that 'cause of Cackletta's Bowser body possession,an egg was made. It was a side effect of the possession. So,it's probably Cackletta his mother...
If you think about,you'll see Superstar Saga and Sunshine (Junior debut) are the same taon (at least in Japan,2002/2003.)