Don't think so, they're usually pretty tight-lipped about outgoing transfers. Might be more willing leak this one as it's a record and generally a pretty huge step for the league.
I think it was a purchase with a loan back, so yeah they have him officially. Dortmund being in the title race meant they weren't going to let him go this winter for anything less then insane money. Guess Chelsea think he'll be Hazard's replacement
Pulisic would've been great at Liverpool, but they outgrew him over the past year. Wild to see any American going for that price, especially with less than a year left on his contract.
No one's going to be shocked if/when any takeover attempt collapses, but there's no reason to think either of those reports are true.
Like said, probably just an Ashley negotiating tactic.