Do they?
My personal impression of the political OpFor is that they cannot really see or hear us at all, let alone understand what we believe or want. They live too much in their own world, and will accuse us of things that are projections of their own ideology.
So no, they don't know that you want to eliminate them permanently - whatever you mean by that. They imagine that you want to flat-out genocide them, based on how they feel towards anyone other than themselves. Remember, they tend to be somewhat... infantile in their thinking.
Incorrect; the Left understands the Right better than the Right understand's the Left.
They do not share the same world view, so they don't reach the same conclusions the Right does, but that doesn't mean they are ignorant that many parts of the Right want permanent, lasting control over society and to never have to deal with anything to the Left of Reagan ever again.
We see it here all the time, and the Left is good enough at infiltration they have agents in far more Right-Wing spaces than vice-versa.
The Left is also good at using undercover agents pretending to be part of the Hard-Right to try to drive that part of the GOP to hinder actual sane policy making on some issues, and to turn normies/Independents away from the Right.
Or did you forget all the glowies and CI's found to have participated in Jan 6th and which keep getting found trying to create 'controlled opposition' groups on the Right?
Nah, the Right has much, much too high an image of itself, it's cleverness, and it's ability to actually understand the Dems in the way the Dems understand themselves and the center of the political spectrum.
The cope needs to end if the GOP wants to be effective.