(a) Expected number of lightbulb failures would be infinity as well if t is allowed to range to infinity (assuming you have an infinite number of bulbs). I suspect they mean a general "t", and this is just a Poisson Process where you are expected to find E[N(t)], where N(t) is the number of bulbs busted by time "t".

(b) Not. . .quite. You are looking for P(A or B < t), which is simply 1-P(A and B > t). Using independence of the processes you should be able to go from here (by relating the CDF to the PDF).

(c) Use (a) with t=3.

(d) Use independence and memoryless property of an exponential rv.