I don't think they take reservations. As for Friday night dinner, unfortunately they close every Friday at 3pm to observe the Sabbath (they stick to having the Sabbath on Saturdays) and I think they reopen on Sunday morning. I don't think there's a particular Christian denomination they follow but if you go there they are pretty friendly, you could just ask them.
It's best to talk to them personally about what they believe. As far as the Shabbat dinner, give them a call at the deli when you know you want to go, or tell them in person if you're there to eat. That way they have an idea on how many guests will be coming that week. Trust me, they will have no problem giving you what information you're looking for whether on person or on the phone and they will be more than happy to have you for Shabbat.
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