No, Peter Parker was long gone by the time the 2099 continuity
began. Miguel O'Hara is Spider-Man 2099.
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It isn't. Spider-man Unlimited was based in the normal
spider-man universe until spider-man hitches a ride into Counter
Earth to capture a fleeing Venom and Carnage. 2099 is a separate
universe and a separate spider-man.
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Spider-Man 2099's real name is Miguel O'Hara. He is a futuristic version of the original Spider-Man set in the year 2099. Miguel gains his powers through a genetic experiment and takes on the mantle of Spider-Man to fight crime in the future.
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The secret identity of Spider-Man 2099 is Walker Sloan.
while
the secret identity of the present Spider-Man is Peter
Parker.