MSSM - One click off a Google Search for "Mt Sinai Internal Medicine Residency" brought me
here, which states that the current intern class has 52 people in it (not all of which are categorical, but there's a ballpark number for you, 2/3 - 3/4 of them are probably cats).
Columbia - 2 clicks off a Google Search for "Columbia Internal Medicine Residency" brought me to
a list of the current house staff. I then took 14 seconds to count the PGY-2 residents (all 44 of them) and now I have the answer.
As for the number of interviews, you'll never see this number in print because it varies from year to year (and is largely irrelevant to your chances of matching). But the conventional wisdom is similar to what applicants are told to do. 10 interviews for 1 spot.
A rough guesstimate then is that each of these programs interviews 400-500 people for their 40-50 slots. Since they're both relatively competitive and sought after programs (esp Columbia), they can probably get away with interviewing fewer people per slot (just like an applicant with Step 1&2 >250, AOA, a PhD and 2 first-author Nature papers can probably get away with fewer interviews than the average applicant) so it's likely they interview more on the order of 300-400 people for their Cat spots.