Can someone drop his middle name and just go by first and last? and is it normal in the US to have no middle name?

Possible. But if you’re changing it go through the appropriate name change procedures (if you’re applying for citizenship it comes with it).

Spouse H4 visa extension, if spouse just change to F1.

No. Just one. .

Late filing of I751

Have to explain why you filed late when you filed it, must be reasonable.

If I win the lottery, will they do interview with me or I will win the green card without any condition?

Sometimes the interview. .

Should I apply COS to H4 before my employer submits H1 withdrawal?

If you never worked for the H-1B employer, you might have a hard time doing COS to H-4 if they RFE for recent pay stubs.

What would be household size if I want to bring my and my wife's parents to US living in same home. We dont have kids.

Have your wife do I-864A and combine your incomes.

Yes, then have the employer do an H-1B for you. A lot of people do that.

Is it possible to reopen removal proceedings after 12 years based on marriage to USC?

Yes. As an arriving alien you can adjust despite an unexecuted order of removal.

Can a European tourist apply for a job in New York?

You can, but then eventually they have to petition you and you have to be eligible (consular processing, or maintain status by getting F-1 etc.).

How can a H4 visa holder transfer to a h1b?

You can do a change of status from H4 to H1B. .