Depends on what visa you came with. If you were (for example) on a student visa for a while, and you decided to get married and adjust status within the US, you should not leave. I myself and tons more did that. However, if you married and filed for a CR1, you need to wait it out outside of the country.
Wrong. If you stay here and file for AOS, you have to file form I 765 and wait until you get your EAD in order to work. If you file for a CR1, once you have the visa and fly into the US, you will be a resident as soon as you land, and thus you'll be able to travel.
Your friend should refrain from giving advice on immigration. Clearly they don't know what they're talking about.