What is the significance of Jesus/Christianity?

To the last point: "Jesus Wept" is a typically British and Irish Catholic expression and is now somewhat archaic in use (my grandparents would have said it a lot but younger people not so much). It is apparently the shortest sentence in the bible - see Wikipedia article - and is something short and easily memorable.

It's origin is from the story of Lazarus dying, before his resurrection, when Christ cried over the loss of his friend showing his humanity.

In actual usage, it has several meanings depending on context but is most commonly another way of saying: "Oh, for God's sake" or something along those lines.

In regards to your first question, if you're referring to the first movie, which is taken directly from Clive Barker, then there is no religious connection at all. The Cenobites are just crazy S&M freaks from another dimension.

Your second question depends on context, which as Ivo already alluded to in his comment, there's a bunch of different Hellraisers. Barker lost control of his concept and it's been given the business by a number of different sources.

Looks like Captain Toad has already answered the third question!