Some terms might be different in different messing applications, but here's what I think you can use.

1 이 채팅방 살아있나요?  (Is this chat group [chat room] active/alive?)

2 이 채팅그룹 아직 활동하나요? (Is this chat group active?)

#1 is probably the  natural way to say it in Korean and one of 채팅방, 채팅그룹, or 그룹채팅방 can be used for the "groupchat".

(채팅 = chatting / chat, 방 = room,  그룹 = group, 살아있다 = active /alive, 활동하다 = active / have an activity)