Budgies are one of the easiest pet birds to sex . If your bird is an adult look at the care (nostrils above the beak). On an adult male it should be blue and a female will be brown . on juvenile birds the male is a light violet and female is a light blue

Yes Cockatiels budgies and many other bird in the parakeet family can be taught to mimic word, sounds and whistles . patience and repetition are impotent . start with simple single syllable word and build your birds vocabulary from there.