If I am playing split screen local will I still be able to invite other friends online??
Using what we saw in the last Panel From Hell as a reference, you should be able to, in the event we first saw two devs playing together using two different computers, and then a third one joined the game in split-screen using a controller.
Can your cop friend do virtually everything I can do or will the host account be the main one? (ecample) does everybody get the chance at romance or just player one?
Your friend should be able to do pretty much everything you can, the only caveat, if things remains as they are in EA, is that each player can only interact with the companions they have recruited, so if you are the one who talks and accepts Gale into the party, your friend won't be able to speak with him. I advice that you each recruit whoever you plan to romance in case this isn't changed for release.
