I do not use Proton in any way (using a trustworthy local provider). But I use a password manager and so I can share my point of view, especially for your question 2. I also can give an general advice about protecting email accounts unrelated to Proton.
Never ever I would trust my passwords anything that requires an email address to use it. What do you do if the service is not available for some reason? I use KeepassXC (which is not available for smartphones I think, but running Linux on phone makes it perfect in my specific case). The vault-file is saved locally on my PC and to decrypt it I only need to select it and type in a password, which should be very strong.
I sync data between phone and PC manually over the home network. I do not create new entries every day, so doing sync manually doesn’t cost much time (just sending and replacing or merging the file).
With password manager I do not see any reason not to take separate passwords. If you password is leaked, it is leaked for both, if you use a single one. If you use separate passwords and your password for your email is leaked → bad for you. But the other way around you protected your email, which also protects many other services that are connected to this address (you know, password forgotten requests of other services). The email address itself should always have a unique password, if it is not used for trash-accounts.