Is ICE waiting until after the hearing, or grabbing people on their way in to the courtroom? Is ICE preventing people being heard, denying them due process? If ICE grabs people, before they are heard, are they held until their hearing, or are they deported on the spot?

Doesn't matter. If you're in the country without legal authorization, you're subject to detention at any time. ICE doesn't have to wait until you have your hearing. Particularly since it's almost certain that your hearing is over procedural matters stemming from your unauthorized presence in the country, which will be de facto probable cause for your detention.

Awful, but lawful.

Who would prosecute? Trump's "Justice" Dept? Red state AGs? Keep the issue tied up in litigation for two years, and the election becomes moot.

States. And the candidates. These wouldn't be criminal cases - they'd be civil lawsuits. Any losing candidate would have standing to bring a complaint that the removal of voters in the process of waiting to vote warrants overturning the election results. The individual voters would also have claims (though I don't know if they'd have standing to seek overturning the election).

The litigation wouldn't be tied up for two years. Election challenges are always handled expeditiously by the courts. An egregious violation like this probably would be resolved between the election and being seated for office - if not, it would be a few months, not two years.