No, it is not necessary.

No.

There are exactly as many **odd numbers** as primes (Euclid, Cantor), and exactly one even **prime** (namely 2), so there must be exactly one **odd** nonprime (namely 1). Cosmologist: 3 is **prime**, yes it is true.... ... 10 is **prime**, 11 is **prime**, 101 is **prime**...

How to prove that all odd numbers are prime

Yes.

And one even number is prime---see Rooster's answer.

https://www.reference.com/math/prime-numbers-odd-5f0c2d756b96b334

No, it's not necessary. The number only divisible by 1 and itself is prime number.