Can Favored Foe and Hunter's Mark be used at the same time? Favored Foe states your concentrating on it 'as if you were concentrating on a spell'. Does that therefore mean you are unable to cast spells requiring concentration as long as you are using Favored Foe?

That's correct. If you cast a concentration spell, Favored Foe will end.

Although Hunter's Mark will generally do more damage, Favored Foe doesn't consume spell slots or cost your bonus action to use.

Quote from InquisitiveCoder >>

That's correct. If you cast a concentration spell, Favored Foe will end.

Although Hunter's Mark will generally do more damage, Favored Foe doesn't consume spell slots or cost your bonus action to use.

 Not to mention, this allows you to diversify your spell selection a bit if you get tired of "I cast hunter's mark and then I attack."

Does it allow you to roll 2d4 for a critical, and does it cost another use to transfer to a new target if foe is eliminated?

Yes the damage increases on a critical. No you can't move it - it's one use per target.