How to install multisite using separate databases?

You don’t. If you want separate dbs use separate installs, maybe with symlinks for one codebase.

The whole point of multisite is to use one database until you get to a few hundred blogs.

OK
is there a way to “for example” allow registered users to check private content on sub.domain.com, but not on domain.com

Yes. You’d use privacy plugins. None of that relies on separate dbs tho. Check the repo.

yes, every page I found about multi WP talks about only one database, but I’m a bit worry about if something goes wrong with one site, the DB is the same, so…
That is my main reason to separate the DB

Do you think is a good practice to have a multi wp, register visitors in sub.domain.com and use Membership plugin to control access to pages and posts?

thanks for your time

but I’m a bit worry about if something goes wrong with one site, the DB is the same, so…

wrong like what? if it’s a plugin, then it only affects that site.

Do you think is a good practice to have a multi wp, register visitors in sub.domain.com and use Membership plugin to control access to pages and posts?

users register to the whole netowrk, then get added to the sub blog. you can use most any membership plugin you want on any of the blogs.

great, thanks Andrea