Yes.
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17 and 68 are not relatively prime because they have 17 as a common factor.
Yes, they are relatively prime.
Yes, 11 and 51 are relatively prime.
To be relatively prime requires another number, and the highest common factor between 17 and that number must be 1. 17 is relatively prime to all numbers which are not multiples of 17 (since 17 is a prime number).
11 is a prime number. For it to be relatively prime, it needs to be compared to another integer.