Correct. Blizzard does not provide live chat as a means of appeal. That has never been the intent of their appeals process. Your only option is to use the ticket system to have a GM double check that your account was flagged for a violation.
No, it is not. However if the gold you recieved is from illicit sources, then THAT is a violation of the rules. Swapping gold is not against the rules, but it is unsupported and they don’t help if things go wrong. Very much an “at your own risk” activity.
The ONLY evidence Blizzard uses is their own logs.
EDIT:
Relevant Blizzard Blue post from a similar thread.