Obviously. Just like how she invented Jazz is October and artists like Nina Simone, Frank Sinatra, etc started to copy her style and cover her songs from C2C.
GaGa's impact on music is actually not big. The impact she had was to make others dress a bit crazier than usual for a couple of years. That's about it.
Nope. Firework was out there way before Gaga's announcement and artists are usually recording the first singles months before the release, i bet we r who we r and ****ing perfect/raise your glass were recorded months before gaga's announcement.