Baam will get all of them like collecting pokemon, even Garam, a man can dream, no? Haha.
Garam was also interested in Baam, and called him cute and not surprised why two princesses of Zahard are following him - I honestly wanted to see Urek reaction seeing Garam liking Baam, and SIU is also hinting on Adori since the end of Workshop Arc, AA wouldn't be surprised until Baam is dating Adori, knowing Baam this might very well happen.
As for this situation, it depends on the translations, I notice sometimes the translations with Rei seems to make him look disrespectful and rude towards beings, but he wasn't necessarily as rude as he actually seems to Baam, and Baam isn't necessarily afraid of him or power as implied or brought up about dying/losing in an instant, which is good.
What I understand from reading it myself is that Traum truly genuinely wanted Baam to become a family member/son in law; while it's true it is easy for people to see Trau want to make Baam slave, the translations if done in other ways or reading the words, doesn't seem to hint there or at least Trau didn't disrespect Baam like that, in fact his gestures and languages have more than treated him as equal, if people were to try to translate themselves from the Korean source.