No, it's not possible.

Each site in MightySites has own usual Joomla backend and these changes can't be applied in frontend.

... Note that it's not possible to share "some" modules or "some" articles, content can be either shared or unique per site as usual. Running an update of extension or Joomla from main site will affect all sites.

You need to know usual Joomla MVC first. Your sites uses same database tables, so for sure changes will affect all sites. Each site should have separate contents, in this case different layouts will be applied. Otherwise you can't ...

... intergrate forum wit light version, too. Am I wrong? Yes, you are wrong. Light version doesn't affect phpBB display, phpBB is displayed as usual.

... each user is registered to and which usergroup each user is in for the Child Site the user is assigned to. Each site has own backend panel as usual, you can only see a list of sites in Main Site's backend, edit their global config and auto-login to backend. I know that in the Main Site, all ...

MightySites can share #__users database table, so users will be same in all sites, but their usergroups (hence permissions) can be different.

Once user logs in any site he will get usual permissions according to assigned usergroups.

... Then I upgrade Joomla on a future date. Do the cloned tables on the slave (parked domain sites)also get upgraded? Only own tables are upgraded as usual. You need to upgrade Joomla in slave site in order to upgrade tables of slave site. If I install a third party component at a later date and the ...

If you want both sites to use same files - you need to point domains to same NS servers of your main site, one site will have own hosting account as usual, and second site should be created as parked domain.

Each site has own backend as usual.

Since users can be shared you can manage users from Joomla 3.1 database in Joomla 2.5 site and vice-versa.

If this is just a form submitted to phpBB it should work as usual, otherwise you can create a special page in Joomla.
You can even use a special bridge method call for creating a new topic in specified forum (please ask Support Center for details).