@Stephen Artzerounian, the quick answer to #1 is no and no, and the quick answer to #2 is yes and yes.
Whichever LLC is going to hold title to the property needs to be formed in the state where the property is located (since that's the jurisdiction in which its legally doing business). So, based on your comment, I imagine you'll have child LLCs in both PA and CT with a parent LLC in CT.
Before forming child LLCs, you'll need to form your parent LLC with you and your partners as members. If the parent company will be in CT, you'll list you and your partners' names in the Certificate of Organization as well as the Operating Agreement.
Then when you form a child LLC in PA, you'll just list the parent LLC in the Operating Agreement, since the PA Certificate of Organization does not ask for LLC member or manager information. Any one of you as individuals can be the Organizer, who is simply the person filing the LLC documents with the state (but is not automatically made a member). Then have the Organizer sign a 'Statement in Lieu of Organizational Meeting' appointing the parent LLC as member. That, along with your Operating Agreement, create you "ownership paper trail".
As long as you create each child LLC in the state where the property is located, you won't have to worry about foreign LLC registration.
Regarding legal issues with the parent: If the parent LLC is used strictly a holding company, you'll mitigate the risk of that entity being sued. You can create another CT management LLC, but some could state that it's overkill. Some might not. Hope that helps a bit.