Question

If you set a permanent HTTP redirection (301 status) then will browsers still visit the old link each time and get the redirection response or wil they know better and change the request URL locally just before performing the request?

Answer 1

It’s not guaranteed, but they are supposed to cache it, and often do in practice.

From the spec:

The requested resource has been assigned a new permanent URI and any
future references to this resource SHOULD use one of the returned
URIs. Clients with link editing capabilities ought to automatically
re-link references to the Request-URI to one or more of the new
references returned by the server, where possible. This response is
cacheable unless indicated otherwise.