The probability of rolling two prime numbers on a standard pair of dice is 1 in 4, or 0.25. Take the probability of rolling a prime on one die, 3 in 6, or 1 in 2, or 0.5, and square it.
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The probability is 5/16 = 0.3125
The probability is 1 out of two. The primes you can roll are 2,3, and 5.
The probability of rolling doubles with two dice is 1 in 6, or about 0.167.
For 6 sided dice, there is only 1 way to get a 2: (1,1). There are 36 outcomes rolling 2 dice; so the probability of rolling two numbers whose sum is 2 is 1/36.
The probability is 11/36.