In that case just use the formula

.

a) You want

b) If the intervals do not overlap, then they are independent, so first find

, then use independence (and stationary increments) to find the result. By that I mean if s_1<t_1<s_2<t_2, then

c)

d),e) You need to look at some stopping times for this, let

. Now what is

? Well, that means by time t, you have had less than n arrivals.

I have no idea to which level you have done things, a little indications of which bits you don't understand would be nice.