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Zero is neither prime or composite but it is an even number because it is between 2 odd numbers which are -1 and +1
Lots of prime numbers have zeros in them. 101, 103, 107 and 109 are all prime numbers. Prime numbers can't end in zero. Numbers that end in zero are multiples of ten and have too many factors to be prime numbers.
No combination of non-zero even numbers can be relatively prime.
There is no name for numbers which are neither prime nor composite.
The question is quite ambiguous. If you're talking about all the even prime numbers between 4 and 50, then the sum is zero. No even number, except '2', is a prime number, so there aren't any between 4 and 50..