You don't need to recommend any policy. Simply saying "I don't support genocide" will illicit a negative response from the pro Israel side of things and puts you in the "against" category.
Sure. But declining to use the term "genocide" similarly illicits a negative response from a lot of the pro Palestinian side.
Single-issue advocates will tend to dislike you if you don't take their position on an issue. That doesn't mean anyone has to. (My pet war was Ukraine. I, similarly, took a dim view of anyone who described Russia's invasion as a defensive war. And I'd similarly argue with folks who thought what happens in Ukraine has nothing to do with America's security, though I hope I was more respectful than the status quo with Gaza.)
These are the people who will determine whether or not you get a visa over a statement both you and I see as benign. Anything other than explicit endorsement is seen as adversarial.
We don't know that yet, the guidance hasn't been issued. (And we haven't seen how it's being interpreted by consular staff.)
Yes. They're publish something and then a picosecond later a district court will issue a nationwide injunction.