No. Children would be 'बच्चे' which is gender neutral. 'बेटे' is 'sons' and 'बेटियां' is daughters.
However while बेटा literally means son, many people use it to refer to both boys and girls, a father could call his daughter बेटा.
उसके* (Though here it would actually be उनके) Yes, you can however generally when you talk about people, उसके / उनके is used rather than उसके पास / उनके पास, the पास form is used more for things you literally own, like items. So familial relations, friends, relationships, when you say things like "My daughters/sons/wife/friend/mother/brothers/etc," it's better to use उसके / उनके.