Good questions. I also have no idea at this time how many guests were at the party and how lavish it was. I'm pretty sure that there were multiple children there to make the "Santa" thing worthwhile so it could very well have been catered. I'm not sure Karr really needed an alibi. He just had to look like he was supposed to be there. I've snuck into places a time or two and if you just hold your head high and look like you belong, most people won't challenge your presence.
Another question I have is whether any parts of the house were off limits. It's a huge house so wouldn't they have tried to keep certain areas private where guests had no reason to be? I realize some hosts never think of those things yet I'm the type that would, particularly if there are small children around.
Finally, if Karr slipped in during the party and talked to JBR to gain her trust, why was she not amongst other friends her age during most of the party and why were those children not supervised by any parents? Would any of those people, even the children, be able to recognize Karr as the person they saw that night?