Peter is not wrong, the engine is (very) largely Ford, although the Jag got VVT which I don't think the Ford's did. Also Mazda, Porche and Cosworth had a hand in it's development, and IMHO, it's one of the best engines I've come across, a real cracker.
I think your mate is confusing the X and S Types, the X was on a Mondeo chassis and uses a lot of Mondeo parts with a transverse engine, the S uses the Jag / Ford DEW platform (Lincoln, Thunderbird etc), used on the XF until last year, and an inline engine, so definitely not a Mondeo.
I can help re the gearbox, as I have a manual