Or you could just add the relevant directive to the top of the .htaccess file directly. For example:
RewriteRule ^([^/]+)\.html$ /product/$1 [R=302,L]
This matches /anyname.html (as in your example), but not /foo/bar/anyname.html.
It also doesn't matter which URL part is changed, except the last one.
So this still shows the content of the original page.
Yes, because your taxonomy's rewrite is hierarchical with the permalink structure /treatment/<term slug> (e.g. /treatment/psychosomatic) or /treatment/<term slug>/<term slug>/... (if the term is a child term, e.g. /...