I can talk about retainers:  I had retainers made from a home impression kit.  Does that make them fake?  I was not retaining anything.  I had the top one made with a shelf at the front like a bite plate.  This was intended to double as a night guard for teeth grinding (actually just clenching).  When I wore it much of the day, it was not for teeth grinding.  After a couple of weeks my bite had improved, so it encouraged me to continue wearing it a lot.  After about five months I could leave it out during the day and my bite didn't regress.

Many years ago I got Hawley retainer-style fake braces.  When I tried wearing these at night, I noticed in the morning my mouth didn't feel right.  I actually didn't wear them that much.  They were not that great a product and my lip kept getting stuck between the braces and the teeth.

I think most likely a well made fake product based on a Hawley retainer would have little effect on the mouth and teeth, but for example home impressions that are not done that well could cause the creation of a badly-fitting appliance and then it tries to distort the mouth.

In terms of them appearing fake, I never wore the fake braces in public and there is no issue with a retainer being there sometimes and not others.

Yes.

My wife has worn fakes for long weekend trips to Flagstaff, Laughlin and Las Vegas, staying "in character" the entire 3-4 days.

Years ago, we also used to frequent a bar (at least weekly) where she always wore her fakes. She ended up becoming friends with some of the staff and would go out with them for drinks, haircuts, etc. She had to wear her fakes every time to keep up the illusion. This went on for about two years.