Is this conjugated to biz? Does it imply that someone is speaking on behalf of a group, or does biz include the speaker and the listener?
Well, for me, not here, sorry. Your sentence is more like an explanation when talking about a departure; the example has a much more general meaning; it is only "see you" :)
Better to memorize those short greeting like sentences, literal translation does not work all the time. Similar one; "you are welcome" :)
"See you!" and "See you later!" are used interchangeably in English.
Why is "see you!" not accepted?
My guess is, that it's because the Turkish sentence here is literally "see you later", with "sonra" meaning "later". "See you" would be just "görüşürüz", which is also very commonly used in Turkish.
I hav always learned görüşürüz as see you later is it used that way colloquially without the sonra
Nope. If you tell a Turkish person "sonra", he/she would not understand what you mean :)
Doesn't görüşürüz already imply that you'll see the person "later", since the encounter happens in the future? It strikes me that adding sonra would specify that you will see someone after a specific event, otherwise you wouldn't use sonra.