Displays your party at GPXPlus.net
You can look in several different places, but the easiest is to check at the top of the page. It will say "Welcome back, (this is your display name)!", just copy-paste that name into the settings.
Yes, it will. Myself i always have an open slot in my party, just in case of events i've missed or The Little Man, or if i find a super-rare event egg in the Lab/Shelter.