Yes, that's an antiquated tax treaty with the Philippines.  Can't tell from the limited info you shared whether your client met all the conditions but we'll assume he does based on your review.  It is apparent your client and the school did not follow the proper process to exempt the treaty-exempt income from federal tax withholding and a refund claim would need to be filed with the return.

FICA already includes Medicare tax.  It consists of both OASDI and Medicare.  These are exempt provided your client is a nonresident alien on a J visa.  You may like to re-read my original post for the conditions, which your client does not automatically satisfy just by being a teacher on J-1.

FUTA is an employer liability and not a concern of your client but, yes, it is exempted under a different section of the Code.

I don't know what j1taxrefund.com is, so can't help you there.  But as I explained before, Line 22 is only there for information purposes and the amount does not get added to the taxable income.