Change User Sign In method from Password hash Synchronization to ADFS Authentication

For Your first question, answer is yes. And because you are probably using -SupportMultipleDomain switch it does not change the other endpoints, which are still configured to point to the federation service.

https://docs.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-install-multiple-domains

So you could change one domain to managed and others will remain federated.

For your second question, it depends on the token life time. The authentication and authorization relies on the token after you have successfully logged in. When the token dies, the sessions dies and they have to re-authenticate but then they will do auth with out ADFS as the domain is managed.

To the third question I don't have an answer but transferring from ADFS to PHS could take up-to 3hrs but but I haven't seen this long delays but just to be on the safe side.

https://docs.microsoft.com/en-us/azure/active-directory/hybrid/tutorial-phs-backup#switch-to-password-hash-synchronization

My suggestion is to use PTA instead of pure ADFS and eventually switch your users to cloud-based authentication if possible in the long run.

https://docs.microsoft.com/en-us/azure/active-directory/hybrid/migrate-from-federation-to-cloud-authentication

Hopefully this helps,