Can I get married to my fiance who's a green card holder with my business visa and stay in US?

You can get married but you cannot stay in the US if you do not have an independent basis for so doing. Marrying a permanent resident does not confer any immediate immigration benefits upon you.

You can get married and she can petition for you, but it will take over 3 years before you will be eligible for Green card through your wife. If you wife is eligible have her apply for citizenship. Once she becomes citizen and you marry her you will be eligible to apply for green card right away.

The fiance petition, Form I-129F can be filed and is available only if your fiance is a US citizen, not a green card holder. Under current law, your fiance, if a green card holder cannot file a fiance petition for you. Instead, your fiance can file a Form I-130 petition for alien relative, but then only if you are a married couple. This option, will allow you to become a green card holder yourself The petition is under F2A category which will take about 30 months to become current. By way of comparison, the F2A petitions that are now current were filed Mar 2011. You cannot legally stay inside the US to wait for the petition to become current; Once filed, you may experience difficulties in entering the US as a tourist because, filing an I-130 raises the presumption that you are intending immigrant, not a tourist. Your concerns can be legitimately addressed through a number of options, but you will need to consult with an experienced immigration attorney on this. Finally, because, you expressed intent to come to the US to marry your fiance, if a border inspector concludes that you are not a true tourist, you may be refused admission during your next visit to the US. Speak to an attorney before you attempt to enter the US under these circumstances.

No, you cannot adjust status until the priority date is current.

If you overstay, you can only get a green card through a marriage to a US citizen. So you will wait until your fiance becomes a US citizen to apply for permanent residency in the US.

Yes. But in order to apply for adjustment of status (green card) and remain in the US after you have married, your fiancee must be a US citizen. She can apply for citizenship on form N-400 if she has been a permanent resident for at least 4 years and 9 months and is a person of good moral character.