Yes, but only with close friends of the same age. If you use it with strangers, you might sound like you're trying too hard or being disrespectful.
The Jakarta dialect is the most widely understood due to its use in national media, but it is not 'Standard Indonesian' (Bahasa Baku).
Only if the listener doesn't understand.
Absolutely not. University essays require Bahasa Baku (Standard Indonesian). Using particles like sih or dong would be considered highly unprofessional.
They are closely related. Bahasa Gaul is heavily influenced by the Jakarta (Betawi) dialect, but it is used by young people all over Indonesia.
Yes, but only with close friends in Jakarta. If you use it with people you don't know well, it can sound 'sok asik' (trying too hard to be cool).