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Fiery Form grants a 4++ (to non-melta) and +2S in close combat.

Does that mean that Ahriman's Mark of Tzeentch improves that save to 3++ (also making him S8 in Close Combat?)

You'd have a save that would get improved by the mark yes.

About the strength I guess ahriman's got a force staff, so yes you'd reach S8

Edit: Just one thing though, you're mixing up 2 different pyromancy powers. There is no limitation to the 4+ invuln, where the second power grants a 4+ COVER save against non melta/non soulblaze hits

Yes.

3++.

Yes, that is exactly how the 'Mark of Tzeentch' works though as noted above you've seemingly slightly confused the effects of two different powers. ;-)