how many universes are exist
No one Knows. By the very definition of the word, there is only one universe. However, some theoretical research in theoretical physics (such as some interpretations of quantum physics) hint that there may be multiple universes outside our own. Some theoretical work suggests that there could be an infinite number of extra-universes, depending upon the theory one is working with. You may want to search for these terms "Many Worlds interpretation of quantum physics", "Everett universes", "Inflation Theory Multiverse", to chase down some of the details.
Also try googling "M-brane theory"
infinite
Currently unknown. When the definition of what continues a universe changes the answer may still be unknown. Remember that your professor is only concerned with you finding the answer he or she wants you to find. The bigger picture is beyond the scope of the course.
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