Can a missionary who is an ordained minister living and performing the duties of a minister in a foreign country apply his SE tax exemption granted by the IRS to Form 1099-MISC income received from his home church?
As a U.S. citizen, the minister is subject to Internal Revenue Code provisions regardless where he lives in the world. But its benefits also apply to him. His Form 4361 exemption granted years earlier when he was a minister in the U.S. is valid. This is true regardless whether he is a Form W-2 employee of his home church (a rare situation for a missionary whose support is not funnelled through a mission agency) or an independent contractor supported by perhaps many sources.
Can he also receive a housing allowance as a Form 1099-MISC missionary?
Yes, the housing designation must be made by the church sending the support. Of course, he must apply all of the standard rules of the Clergy Housing Allowance Clarification Act of 2002 in order to exclude this support from income tax.