1) Certainly they have rights, including due process. Can non-citizens be accused of murder, taken to the nearest tree, and hung without due process?
2) For legal visas, if they violated the terms and conditions, then they should be deported. But specifically in this situation, she is being deported for opposing the Israeli government.
3) Come on, man! (Read in Joe Biden voice).
Exactly. And there is a process. In general, when there is reasonable and probable cause that people are in the nation illegally, they are detained. They are released when they show evidence that they are legal. It can happen in 10 seconds by showing a valid ID, or it may take a day or two to provide evidence. If not, then they are in line for deportation. This is not hypothetical. This is from recent incidents locally.
In the unlikely case that an American citizen is deported, they can return as soon as they show evidence that they can legally enter.