Your fiance needs to become a permanent resident first. If she enters the US on a tourist visa with the purpose of getting married, it will cause a very serious problem. Consult with an attorney.
It's possible. But, there's also the possibility that USCIS may accuse your fiancee of committing visa fraud if they believe she had a preconceived intent to remain permanently when she entered the US with a nonimmigrant visa.
If you marry her while she;'s here and she stays here and you file for the green card, she can certainly get the green card much faster here, than abroad.
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