Yes, the bridge 5.2.1 works with phpBB 3.3.12
You can upgrade phpBB as usual.

the definition text can contain usual HTML code which can be next displayed in the report table but having column setting "HTML Template" as "{raw_value}"

FYI: the light bridge version works with Gantry now. Usual p8pbb bridge doesn't and currently, there is no way to make it compatible.

... extensions/administration/multisites-manager/case-studies/sharing-database-data-between-existing-independent-websites. All sites are separated (usual Joomla installations with own files and database) but all slaves will load users, usergroups and access level tables from master site, hence these ...

Please create a ticket in Support Center to add custom components.

Advanced Module Manager has own table for modules, if usual Modules are overloaded and Advanced Module Manager is used, it should be also overloaded.

No, it's useless, in any case you will not see anything special - just a usual website.

... have to be done directly at the database? You can delete slave site in MightySites, next delete its menu item, article and modules in Joomla as usual. I assume only the main site, on which the component sites, can be replicated? You can’t replicate a pre-existing subsite to become another i ...

Will mightysites work with a url including the port? Example:

https://subdomain.testing.site:1337

Would it need additional configuration beyond the usual domain setup?

Bridge installation takes 5 mins, but note that it requires presence of phpBB itself. phpBB installation also takes 5 mins.

We provide free installation.

Yes, phpBB is displayed inside Joomla template, just like usual Joomla component.

Yes, it requires usual phpBB installation in 1st level subfolder like /phpBB and it's just a bridge.