Yes, you may study in the U.S. on K-3 visa while awaiting the issuance of an immigrant visa.
No, you may travel outside of the U.S. and re-enter on your K-3 visa. If you have filed for Adjustment of Status in the U.S. prior to your departure from the U.S., the USCIS will not presume that the departure constitutes abandonment of your adjustment application.
To apply for a K-3 visa, your U.S. citizen spouse must:
Note: Confirmation of USCIS approval of the I-129F Petition for Alien Fiance is required before a K-3 visa may be issued.