For the first question, use the cdf.
But I don't know what a logistic rv is...
Also, what have you tried ? Because you posted several threads without showing anything :|
(a) Show that both -logU and -log(1-U) are exponential random variables
(b) Show that X=log(u/(1-u)) is a logistic(0,1) random variable
(c) Show how to generate a logistic(m,b) random variable
SAS or R programming can/should be used to complete.