There's not really any way to explain why certain words are with chat in these situations, except that they've evolved through the internet age and are just how we say it, now. So there is no source or reference for me to give you, except that this is standard usage:
I am currently in a chatroom.
I am getting on Skype (or other chat provider).
I asked him a question on chat the other night.
I asked him a question on/over Skype (or other chat provider) the other night.
To speculate as to why these patterns came about:
It's likely that you are described as in a chatroom because it contains the word room, and if we take the abstract concept of a chatroom and consider it a physical object, then you would always describe yourself as in a physical room.
You get on/log on to a chat provider similarly to how you log on to any other website; it's just how it's phrased, I don't have any speculations as to the etymology.
Perhaps we talk on chat because while on chat we are online, or because the text we type appears on the chat window.
When referring to the chat provider by name instead of the generic chat in general, perhaps we can use over similarly to how we can say over the phone; we're imagining the chat provider as sending our messages across, or over, their network.
At any rate, the above is just speculation as to why these usages are prevalent. Just stick with the rules and you should be fine, I doubt there will be a pop quiz on the origins! :)
First, when you say:
German-American
it means your *ethnic" background is German (meaning your ancestors at some time were from Germany), but you were born in America. Or you were born in Germany but now permanantly residing in America.
This should apply to any nation specific usage.
As for:
African-American
this is more general. It could be like "European-American".
Such a person (or their ancestors) would be (or would be perceived to be) from that region of the world. I think we all know the general criteria used, but that is another discussion.
Best Answer
As you correctly stated in your question, when you are describing movement towards a destination (in your example, the verb 'go'), you use the preposition 'to'. Depending on the destination, the article 'the' may also be required.
If you are describing a 'state of being' (for example, the stative verb 'to be') when referring to a destination, the preposition 'in' is used.
I am in Miami. (state of being)
I am going to the living room. (movement)
'Going in Miami' or 'going in the living room' would be incorrect in my opinion.