Yes, you can get married. He will have to apply for a "Change of Status" before his current status expires. Consult with an immigration lawyer asap. Good luck!
This answer is for informational purposes only and should not be construed as legal advice.
You may marry legally, however, since you appear to be rightfully concerned about your pending immigration visa and your future spouse's presence to remain lawfully in the United States. Also, it seems you desire to do everything legally correct. If these premises are correct, promptly delegate any of your pressing issues to the counsel of record, who has all the case documentation and is intimately familiar with the case's details which is the only legally appropriate measure under your narrative.
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