the number of united states universities?

Answer 1

This is difficult to answer because there are so many and many can be small. But, the review guides (US News and World Report or Princeton Review) typically limit their list to the top 400 or so.
When you add up Universities, Colleges, and Technical Institutes, there are likely close to 1000 schools that offer 4-year degrees. There are many more if you include trade schools or community colleges that offer Associates degrees or other 2-year degrees.