I don’t know the answer to the logistical questions asked, for certain.
The answer for 2 is simple, the Vatican doesn’t have the social services or facilities to house, long-term, many more than that. While it did hide Jews during WWII, the conditions were less than optimal. Also, Vatican City is only 13 acres. Finally, the Pope asked each Catholic entity to take in one family. It has lead by example and taken in two.
Not enough room? How convenient for them.
Why not donate about 90 percent of all proceeds and assets from the church to all the poor countries?