Shortcuts/basics to know?

I'm not really sure why you want to memorize all this stuff in the first place. I didn't memorize most of the things you listed below since most of it is unnecessary. Here are my comments:

1. Prime numbers up to (and not including) 100
You only need to know the prime numbers up to about 30. Often, the trick is to recognize a prime number or know how to determine whether a number is prime. I do not recall the formula off the top of my head, but you can find it online.

2. Factorials up to 7
Just memorize them straight.

3. Decimal equivalents of fractions (and vice versa) with denominator 2, 4, 5, 8, 10
2, 4, 5, 10 should be easy. I'm not sure why you want to know the equivalent for 8.
2 - if the numerator is divisible by 2 then the decimal portion is just .0; otherwise it's .5
4 - just remember 1/4 = .25, 2/4 = .5, 3/4 = .75, 4/4 (divisible by 4)= .0
5 - .5 or .0
10 - the numerator is the decimal. 1/10 = .1, 2/10 = .2, 3/10 = .3, 15/10 = 1 & 5/10 = 1 & .5 = 1.5

4. Factors of 36, 48, 72, 96, 144
You don't really need to memorize these; just be sure you know how to factor the basic numbers and then on the exam if these numbers come up you can build a factorization tree. The numbers you should memorize include: 4, 6, 8, 9, 10, 12. All the rest (non-primes) are combinations of primes and the factorizations of these numbers.

5. Powers (up to): 2^10, 3^5, 4^4, 5^4, 6^3, 7^2, 8^2, ... , 19^2
The even ones you don't need to memorize because of the exponent rule - 4^4 = (2^2)^4 which can be simplified to an exponent of 2. Honestly I don't think you need to remember any powers except for the first 10 powers of 2 and maybe the first 3 powers of 3/5.