No, they are the only numbers that are NOT rectangular in shape. (I think you knew this and screwed up your question.) That is, all non-primes can be arranged into the form of a rectangle - e.g. 21 can be organized as a rectangle with dimensions of 3 x 7. But prime numbers cannot be organized as rectangles.
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There is no such formula. Rectangular numbers are composite numbers and there is no known formula that will generate either composite numbers or prime numbers.
No. To be rectangular a number must have two factors greater than 1. If it has two factors greater than 1, it cannot be prime.
101
The second and third rectangular numbers are 6 and 12
The prime numbers and the squares of primes between 2 and 20: 3, 4, 5, 7, 9, 11, 13, 17 and 19.