Some of them are: 11 13 17 37 and 79
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Prime numbers that are still prime after their digits are reversed, like (13,31)(17,71)(37,73)(79,97)(107,701)(113,311)
61 42 56 89
11 13 17 31 37 71 73 79 97
Prime numbers with hundreds of digits have been found, but there are still more to come that haven't been found yet. It's not possible to add up all the prime numbers, because nobody knows what they all are yet. Since there is no last prime number (this was proved 2000 years ago by Euclid), the sum of all prime numbers is infinite.
Yes. Being a prime number has nothing to do with the decimal system.