Containing him to Silvermoon would be seen as a hostile action on behalf of the Blood Elves. Also, the purpose of the alliance was Blood Elves needing assistance. It's natural potential allies would check out how dire the situation is and how much assistance is needed.
Again, he randomly sent Dwarves to another continent to mess with stuff, even though there were plenty more potential digsites in EK (and even in Kalimdor there were areas they could dig at that didn't belong to the Horde). There's not a lot to support him being against randomly messing with stuff. Especially when the stuff was already aided by the Forsaken (that were in conflict with Dwarves of Dun Garok) and was in talks with the Horde that he was explicitly not against messing with. Which kinda is a reason already.
Why would it be wiped out with him? Just as he assumed command because he was the highest ranked surviving officer, someone else would assume command after him. Stormwind just assumed political control afterwards because they were the strongest remaining party.
What high ranking Blood Elves dissented? What high ranking Blood Elves were killed by Garrosh? And just like Vereesa and Alleria may not know certain things, there's no indication anyone among Blood Elves realized Garrosh knew of their peace talks with Alliance and used the Sunreavers to steal the Bell specifically to fuck those talks up. Without that knowledge the theft of the Bell is simply a military operation Garrosh had the right to undertake as a Warchief of the Horde.
Theramore was a justified target of war and the alternative was putting everyone in it to the sword, the person who bombed a Druid school was executed by Garrosh himself, Earthen Ring including the former Warchief was explicitly against the abuse of elementals (and given how it's cross-faction organization the Alliance members knew that) and the only enslavement of Pandaren came from individuals corrupted by the Sha and happened on the Alliance side as well.
The Blight was created with Scourge in mind. But just because Scourge was dealt with doesn't mean the Forsaken should drop a potent weapon (that isn't prohibited by anything on Azeroth). If the Alliance have a problem with being a target of the Blight they can not start a world war against the Horde. Given the aggressor in Silithus quests, they seem to be OK with being the target of Forsaken though.
She starts blabbering about Anduin immediately after greetings with Lor'themar. So unless there's a hidden time skip in that questline, yes, she does. And while she did mention wanting to meet Sylvanas in one of the datamined files, she mentions "HOW CAN SHE LEAD THE HORDE?!?!?!" three times as often. She also seems to have preconceived notions about Sylvanas already and wasn't particularly friendly towards her when she mentioned her to Lor'themar.