As for mirroring, I think most managers/bosses would've heard of that by now and would be mostly creeped out by it, not like it's familiar. I can kind of understand why fidgeting would be a problem in a lot of offices or anywhere. If you're fidgeting and your coworkers are trying to concentrate on their work, it could be really distracting. For me personally, it is. I had a coworker shake his leg all day, someone else would twirl hair constantly, if I didn't know better I'd think they were trying to distract me. I think the reason it's bad to put on a mask just to get a job, unless you intend to keep your mask on the entire time you work there is, it seems like you're lying. If a friend lied to me just to get me to be friends, and then I found out later they were just lying, I'd probably keep my distance at least emotionally. In other words if you use some techniques to hide something about you in an interview, and then change, your boss and coworkers will probably think well we can't trust her/him. I kind of wonder if it would help to just walk into an interview and explain I'm autistic/aspergers, so they're not just wondering what happened? Not making it a big deal, just factual. Personally, I don't think you need to be an exact copy of all your coworkers, in fact I think most bosses actually try to have some variety to use each person's strengths. You need some people to be good at research, or data, or public speaking. Otherwise, what do you need all those people for anyway?
As for ties, I thought it was like some women wear scarves. Not required but I guess button up if you're not wearing those. Who knows, maybe they used ties/scarves to close a shirt kind of like some coats don't have a top button but a big collar, so you use a scarf.