Based on different combat unit affiliation patches, I'd say neither are active with either of the units on the right sleeve (1st Cav and 1st Armored BDE) with those not seen on the left sleeve. TNNG/278th very possible.
That really has no bearing on anything...Theyre wearing ACUs which means that pic is no earlier than OIF4, which means they could have easily been in OIF2 with each unit and PCS'd and deployed again with another.