Are there any laws and or regulations prohibiting foreign doctors from performing medical procedures at a foreign hospital when deployed?

There is no were near enough information available to answer this question

The laws you need to worry about are the laws of the host nation and the UCMJ. For the UCMJ if the command approves you are fine. For the Host nation it depends if their medical governing body recognizes their credentials and they want them preforming surgery.

Think that question through
Why/how would an Army regulation prevent a foreign doctor from working in a foreign country? Army regulations only apply to people in the Army.

Your post is missing way to much info.