I really doubt that Murkowski caucuses with the Democrats, but she could easily become an indy and run to caucus with the Republican's.
Probably. She's not a Democrat at heart, but she would be accepted into the party. I'm not sure being an Independent Republican can save her. Her numbers are horrific amongst Republicans. Her best bet is probably to go Indy and promise to be an Alaska Independent or something like that. That could mean caucusing with the Democrats for the current Congress. There is no path for her to win through Republican voters. She needs independents and Democrats.
She'll need some moderate republicans ( and center right/ right Indies) to win in 2022. I dont think saying I'm going to caucus with Schumer in an R year is the best way to do that. I think she should just go true Alaska indy as you say
