Some of us do hold advanced degrees, mine happens to be in law. As someone who went to law school after a few decades professionally developing software I am both a developer and a legal expert. 
As a legal expert I can answer your question quite simply.
“Will Twitch sue us?”
Only they can answer that. Anyone can sue for just about anything, a prima facie case is not hard to muster. Arbitration is mandated in the TOS but there are other avenues off the top of my head 18 USC 1030(g) comes to mind.
Nothing mandates that someone sue if they have cause. They can simply say “nope we dont care.” With that said failure to protect certain IP assets can result in losing the rights to them in the future. How and where you use their logos, etc will be something that piques their interest - especially by removing the iframe which lets them make it clear its their content not yours.
Having had a few discussions with twitch legal I can tell you their (public) address is legal@twitch.tv although sometimes they dont care about answering that. Lawyers really do not like to ignore letters mailed return receipt though. If you cant get hold of them through any other means that may be what you need to do.