Since the denominator in question 1(b) is (2n)^1/2 can I still use the p-integral test? or does it just have to be n on it's own to use that test for comparison?
It has to be "n on its own"; that is not hard to achieve, since (ab)^n = a^n b^n. (Your question is somewhat unclear, so I may be misinterpeting it.)
Question 1 c), cosn is always positive but never increasing or decreasing cntinuously is this sufficent to be divergent or is there a test?
cos(n) is not always positive; it is sometimes increasing, sometimes decreasing; that is not sufficient for the series to diverge (since the terms of the series involve not only cos(n); yes, there is a test, but you are somewhat off the track here.
Sorry I meant cosn + 1 is always over 0 and less than 2, but is sometimes increasing and sometimes decreasing, so do you compare with say 3/n?
Yes, comparing with, say, 3/n is a good approach. It does not matter at all if the terms are decreasing or not when you use the comparison tests.
Is 3/n same as 1/n?
They are not the same. You probably want to ask something else here. [Upon seeing the question again (I forgot it one moment; it is good to post the question when you want an answer): why would you want to compare with 3/n? The denominator in the terms of the series in the problem has n^2, not just n.]
I know it is n^2, and I should ask if 3/n^2 and 1/n^2 both converge?
Yes, they do.