By raw Yes or No
By the description on page 216 of BG-DiA, An infernal war-machine is "manufactured" and "made of iron". Thus it is a manufactured metal object, thus a valid target.
However it also states that "An infernal war machines statistics function like those of a creature", meaning you could argue they count as creatures. So there is some DM discretion on whether or not to treat it like a creature. So ask your DM if they are treating it like a creature it is a valid target for creature targeting spells If they are not then it can be targeted by heat metal.
This could be argued both ways. It says, "like those of a creature", which would imply treat like a creature. But at the same time, function like a creature, would imply it is not a creature and it should be treated more like a wielded magic item.
Personally I would lean toward treating them as creatures, there is a balance aspect, many spells cannot target objects, limiting how you can fight one.
If treating it as a creature it cannot be a target for heat metal.
Now assuming your DM says they are treating it as an object, then some of your other questions can be answered.
Note that nowhere in the spell does it say the object takes damage so the vehicle itself will not be damaged if it is a object.
Can they continue to pilot it:
Well you can continue to holding a sword it has been cast on if you succeed your save, so you should be able to keep piloting if you make your save, you will just take damage every round. I would also argue that much like armor you keep taking damage is you stay inside it, so internal passengers would flee or take damage. External passengers can simply let go like a weapon of shield. But this gets into the gray area of what happen when you cast it on an iron ladder someone is climbing or on an iron cage with a prisoner? The spell leaves a lot up to the DM.