I've lost count of the number of times I've accidentally clicked "Make Leader" instead of "Beam to Ship", and however many times it's been I've topped that with the number of times I've accidentally left the party clicking my own icon to beam to my own ship. It would be so much easier if there were a simple shortcut - say, shift+click on a character portrait - that would always beam to that character's ship (even your own) provided you are in a place that you can beam from. Also, right now I can't think of any reason for hosting a server except for cooperative play. It doesn't make sense to me that people aren't automatically put into a party when they join a server. Maybe there could be different modes of play down the line where not being in a party might be called for (or where being in different parties might make sense), but right now it's kinda weird that when having someone join a server there's this awkward extra step of having to invite people to a party as well.
To add to your suggestion, the ability to make the window disappear again when you click on a party member's portrait. Currently if you click on them you have to select an option before the window disappears. This is ridiculous if you accidentally click the wrong person
I'm pretty sure the window not going away will be dealt with. I was pulling my hair out from the search-field being active by default in windows. But that got fixed sooner than I expected. Pretty good ideas though. There's quite a bit of interface streamlining to be done what with all the shortcuts and keybindings being limited to the bare essentials currently. Hopefully your suggetions will be part of the process in some form or another