Let's try :)

• For Mario. The first line 1 implies that Mario = 10. From the second line we then deduce that Yoshi = 5. The third line then implies that the dragon (forgot his name) = 4. Therefore, 4 + (5x10) = 54.
• Now the primes. The possible remainders of a division by 5 are 0, 1, 2, 3 and 4. We here focus here on the odd remainders, i.e. 1 and 3. The relevant prime numbers can thus be written as P=5n+1 or P=5n+3 for n being an natural number. For n=0, we have thus two options, P=1 and P=3. Since 1 is not a prime number by definition, we are left with P=3 as the only solution. For any other value of odd value of n, we end up with P being even and thus not primes. For the other values, we have as acceptable choices: 11, 13 (n=2); 23 (n=4); 31 (n=6); 41, 43 (n=8); 53 (n=10); 61 (n=12); 71, 73 (n=14); 83 (n=14). That's it. Total: 12 prime numbers whose division by 5 does leave an odd remainder.
• Now the knots. From the first equation, one gets 21=1. Therefore a hidden operation may be (mod20), (mod 10), (mod 5), (mod 4), (mod 2). Applying this at the second equation, one has as possible answers: 12, 2 or 0. Strange. I don't know here. I would say that the problem is ill-defined.