I've never heard of applicants being put on a waitlist before attending the interview...I've only ever heard of schools putting applicants on the waitlist after they've interviewed (and decided they would even want to accept those people...after all, waitlist implies that you would get in if the people who got offers turned them down). I can't really see a POI accepting someone into the program after not inviting them to the interview weekend...it's just too big of a risk without having met the person first (unless, of course, those arrangements were made ahead of time and the applicant did a Skype interview or something like that).
As far as how many applicants are invited to interview weekend, it's clear from others' posts that it varies widely across programs. My program invites 40-45 people to the open house, which is a 1.5 day event. Some POIs invite more applicants than others (I happen to know that one of the professors in our department only invited two people, while others are inviting 5-7). But, I think inviting only two people to interview is pretty unusual, and I think the most common number is 5-6 per spot (and there are 8 spots available).
Edit: Some schools will actually list on their website how many people received offers vs. how many people accepted offers...so if you know how many people they invite to interview, you can figure out roughly your chances of getting an offer after you interview. That said, this likely varies from one school to another and also from year to year in one school...it's possible that one year a lot of applicants turned down first-round offers for that school (and therefore several people get in off the waitlist), but it's also possible that all 8 people who got first offers accepted right away.