The hotel (sleeping) rooms, and all social interactions planned within, are not part of the Eurofurence Convention. We merely provide the booking for them, and ask all attendees to abide the hotel policies, especially so that the convention as a whole is kept in good memories also from the hotel staff. So sure you're allowed to invite people without EF badge to visit your room. They may not, however, sleep there (or anywhere else inside the hotel) during the night, which is called "ghosting" and forbidden.
As far as I'm informed, the Piano Bar and hotel restaurant is also 'public area' during their normal opening times.
The question about day tickets you should email to reg@eurofurence.org
*purrrrr*