My sister filed petition for me last year maybe I-130. I am an Indian and my wife is Italian, I am in California nowadays since last week. Can we stay here permanently under I-485 or AOS whatever?
That category takes 13-14 years. During the time you are waiting for your priority date to be current, you cannot stay in the USA just because your green card is pending. You can, however, stay or come to the USA under a visa independent of the green card such as L-1, H-1. You can also apply for a green card in several categories simultaneously.
Can I get K visa for my spouse? I am a US immigrant with green card. Is there something called a V visa?
V visa no longer exists. There is no K visa option for green card holders. Sorry.
Last year my tourist visa was denied because the officer thought I may not come back. Now I am going for student visa. What effect will the tourist denial have on my student visa application?
When the tourist visa denial is based upon a possible intent to immigrate (also known as INA Section 214(b) denial), it CAN be a problem for student visa.