Please please help me through these questions. These might look simple but I am confused about whether these are independent distributions. What does it mean by saying two RVs have the same distribution?

(13) Let X and Y have the same distribution Poisson (1). Does X + Y follow a Poisson distribution? Explain why. (14) Let X ~ N(0, 1) and Y ~ N(0, 1). Does U = X + Y follow a normal distribution? If yes, find the numerical value for Var(U); if not, explain why by providing a counter-example