Exhaust smell comes through vents only when heater is turned on
Apparently the HVAC fan is pulling-in fumes from… somewhere. I would check for oil leaks under the hood that are being vaporized by the hot engine, because oil fumes are frequently mistaken for exhaust fumes.
If there is no oil leak, then you have to assume that you are smelling exhaust fumes, and that is definitely dangerous for you and your passengers. An exhaust leak could be coming from the exhaust manifold(s), or from the exhaust pipe, and I suggest that you have a mechanic or a muffler shop check-out the source of the problem before you and your passengers wind-up with Carbon Monoxide poisoning.
If you do hear an exhaust leak, places to check around those year trucks are…
the exhaust manifolds tend to get pin holes in them. The manifold gaskets leak, the EGR tube running from the top to the exhaust manifold tend to rot out. the connection from the exhaust manifold to the exhaust pipe can leak.
Might be worth the time to read about the problem of exhaust entry into Ford Explorer cabins.
On that vehicle claimed to involve “bumpers and tailpipes, the sheet metal panels and overlaps, the rear air extractors, and the auxiliary air conditioning systems.” Probably unrelated to F150, but might find something useful.