If I get mortgage loan from a private person overseas to finance purchase of a rental property, is my interest payment of this loan tax deductable?

Yes, provided you report to the IRS exactly to WHOM you are making these payments.

You may also need to withhold 30% tax on the interest portion of the payment (see Sec. 871 (a) and Form 1042), unless a treaty applies or the loan qualifies for the portfolio interest exception. Sec. 871(h).

You may also need to withhold 30% tax on the interest portion of the payment (see Sec. 871 (a) and Form 1042), unless a treaty applies or the loan qualifies for the portfolio interest exception. Sec. 871(h).

Is the withholding requirement still applies if the property is for personal use and not for rental?

Yes, the withholding applies even for a loan related to personal use property. Technically, the loan stands alone (separate from property which may secure the loan).