No, they do not. If one of the prime numbers is 2, you will have an odd number.
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Two is even and it's a prime number. All other even numbers can never be prime though because they will always be divisible by 2. So in fact, not all prime numbers are odd, but 2 is the only even prime number.
Not quite true . . . the number '2' is a prime number. All the rest of the even numbers cannot be prime because they always can be divided by 2.
Prime numbers, except 2, are always odd (they would not be prime if they were even cos they would be divisible by 2.) 1 less than any odd number must be an even number.
No, as all prime numbers are odd, excluding 2, and when you add two odd numbers you get an even number. This even number can't be a prime number as it will be divisible by 2. 101 and 31 are both prime, but 101+31 is 132.
You don't always. 2 + 5 = 7, for example. But all prime numbers other than 2 are odd and two odd numbers always equal an even number when added together.