First thing to notice is that the terms alternate in sign, so the n'th term will have to have a factor in it. Then it has a power of x, starting at in the n=0 term, and going up by 4 at a time. So the n'th term will need a factor . Finally, there is a factorial in the denominator, starting with 1! in the n=0 term (although that doesn't explicitly appear there), and going up by 2 at a time. So the denominator in the n'th term should be . Having done all that, you should be able to write down the formula for the n'th term (and check that it gives the right answers for n=1,2 and 3).
For problem 2), you are supposed to spot that this is the value of the series when x=2. You are also supposed to recognise this as the Taylor series for a familiar (trigonometric) function. That should enable you to write down the sum of the series.