We don't have separate demo site and current site is fine, please double check at your side.

Your server provider should setup certificates, it's not easy: each parked domain should be recreated as separate virtual host in apache config.

... data is suspicious. Usually slave sites have most of master's database content. If you want independent Jomsocial - better have it in own separate hosting account.

MightySites doesn't synchronize data, it shares data: both sites will use same database tables.

Single login will work for separate sites, but they all should share users.

... site). Does it mean data will be syncrinized between 2 database ( user data only) or slave site will use data directly master database? For 2 separate installed joomla site still single sign on will work ? Thank you :)

Yes, MightySites allows you to have separate cache path in advanced site settings.
If template follows standard Joomla cache path - it will be separate per site.

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 use different layouts, or create a single layout override and display ...

You can create separate layouts per site and configure them in component settings if component has such settings and its config is not shared.

Is there a way to use separate favicons for each site?

Does this mean it can do one OR the other, or can do BOTH at SAME time. And is it interchangeable. It can do each task separately or both at same time. For example Lets say I configure it as "Sharing Database" but then want to change it in the future to "use same files ...