I feel bad for you if you're doing this for a class, your questions rely on constructions of gender and sexuality that are silly and juvenile. If you peddle this shit at a university your professor will fail you. Anyone who understand research methods will fail you.
Find something less stupid to ask questions about.
Of course gender roles are sexist, by definition they are necessarily sexist. In practice they are also sexist. Gender roles are attributes and behaviors that society attributes to one gender and does not attribute to the other. This is basic tautology, in my opinion. If you accept my definition, or even my characterization of gender roles, than you cannot logically reject my conclusion that gender roles are necessarily sexist given the standard definition of sexism. Gender roles and sexism are indistinguishable.
As for who gets away with more lying? Are you kidding me? All this is really asking the me is am I as sexist as the person asking this question? You're asking me to attribute behavior with a negative connotation to one gender over another. Too bad, all people regardless of race, class, sex, religion, gender, sexuality, et al lie the same amount on average. I'm pretty good at manipulating people do to what I want, but I don't need to lie to get them to do it, manipulation is different than lying.
You can't make (unprejudiced) generalizations about the actions of specific identities as groups (ex: gender, class, sexuality, race), you can make statements about the actions of individuals.
Guess what? People will date people who ask them out. If a person doesn't ask a person out, they won't be able to go on a date with that person.