If the section asks about information about your last travel to the U.S., then you should provide the passport number you used when you last were...

If you are eligible for a work permit because you have a pending application for adjustment of status, whether it is employment or family based, in...

It is real. You can sponsor refugees abroad to come to the U.S. Check the Department of State website.

If she gets a visitor's visa she can be admitted up to six months at a time. She can also file to extend her stay.

While there is no rule against it, it is highly unlikely a consular officer would agree to issue you such a visa.

Yes, you could provide an I-864 from a joint sponsor at the interview overseas for the immigrant visa application.

You can buy a home and take a job in the U.S. and come back to it every five months, and stay in the U.S. for a month. Or you can just file for a...

It seems to me that renewing your passport should not be a basis to deny your application for asylum.

Perhaps you mean your I-551 stamp, and not an immigrant visa? An I-751 is not an application for adjustment of status, but it is an application...

I think your chances are about 50/50, but the only way to find out for sure is to give it a try and file the application.