See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
1. Normally when you have a green card application pending you have exhibited immigration intent. You’ve clearly told the government look I want to live in the US. So filing of a green card is exhibition of an immigration intention. However there are certain kind of nonimmigrant visas that are immuned from the poison of immigrant intent. Those visas are called dual intent visas. Dual intent visas even though they are nonimmigrant visas allow you to have a green card application either filed or almost approved or pending , is no problem at all. L-1 and L-2 are examples of dual intent visas as are H-1 and H-4. These are the visas were even if you have a green card going there is absolutely no problem.
But tourist visas, student visas, exchange visitor visas like J visas, H-2B visas - these visas do not allow you to have an immigration intention. E-1 and E-2, E-3 are kind of ok. It is pretty complicated but overall they are pretty much to the level of dual intent visas. G visa which is for World Bank employees and international organization employees are also dual intent visas. K visas are dual intent visas. M visas are not dual intent visas. P and Q not dual intent. R probably is ok to have a green card going.
It is important to understand the distinction between dual intent visa which allows you to have a green card going and single intent visa which does not allow you to have a green card going.
So if you have a green card going and you apply for a tourist visa that can be denied. Not necessarily but can be denied.
2. There are certain things that can be done and I think one is called survivor benefits and the other one is called humanitarian reinstatement. Sometimes those two things can be of use. Look that up if something is not clear.