No, you do not need to notify the Federal IRS or state tax system when you move overseas.
In 2014, an eligible foreign worker can exclude up to $99,200 of income from federal income taxes. Read the Foreign Earned Income Exclusion Tax Memo and speak with your tax advisor for more details. Be sure to submit an accurate W-4 form to GCM to avoid having too much federal income taxes withheld from each paycheck and receiving a large income tax refund when living on a needs-based salary. The current international SGW assumes you will not be liable for federal income taxes.
3. Does accepting parsonage as an Ordained Minister lower the person's Social Security and Medicare tax liability?
No, the pastor would still have to pay Social Security and Medicare (15.3% total) on the parsonage as well as on their taxable income. For most overseas staff if they qualify for the Foreign Earned Income Exclusion, the parsonage does not typically lower their tax liability since the Foreign Earned Income Exclusion exempts them from paying federal income taxes on any earned income under $97,600 (as of 2013).