I think that beszelget would be better translated as discussing than chatting, at least for American English purposes
I thing "discussing" needs an object, doesn't it?
"Beszélgetni" is to chat, to have a chat/talk/conversation.
No, beszelget doesn't mean discussing. "Megbeszel" would be a better translation of "discuss".
Yep beszél = speak e.g. speak a language vs beszélget = to chat. There are lots of verbs that can be modified by 'gat/get' (known as the "frequentative"), and it usually implies repetition over time or without specific purpose, but it can change the meaning of the verb significantly e.g. hall- to hear vs hallgat to listen.
In the correct solution there is a mistake. In the phrase "Where are do you talk" "are" should not be there
If you're interested where another person has their chats.
It can also be a particularly rude way of telling someone to stop talking because the place they're at ot the situation they're in (such as being at work &c) is not suitable for such activities.
No. "beszélsz" means to you speak while "beszélgetsz" means "you chat" ie speak continually or with low value. The "-get" is used to modify verbs quite commonly in Hungarian. It adds the idea of repetition or weakness.