In Wayne’s World is Wayne telling Stacy to get the internet?
No.
“Get the Net” isn’t really directed at her. It is a call to imaginary people to bring a literal net to capture her and take her to an insane asylum.
This was before the internet had become ubiquitous. It’s the net for catching an escaping mental patient.
Yes, I seem to recall it said in at least one of the SNL skits as well. But in the opposite context, trying to date a girl and calling for a ‘net’ to try to land the fish he’s struggling with.