Since Rhodey is a War Dog in this fanfiction, the plot could revolve around his missions. He might be assigned to protect a certain asset, or infiltrate an enemy organization. Along the way, he could face betrayal from within or have to make difficult decisions that would impact not only his own life but also the safety of others in the Marvel world.
One interesting aspect could be Rhodey's character development. Maybe he has to face new challenges as a War Dog that test his loyalty and courage. For example, he might be sent on dangerous missions alone and has to rely on his wits and combat skills to survive.
Definitely not. Rhodey's character in the comics was never depicted as a Skrull. His role and development were consistent without this element of transformation.
One possible reason could be a misunderstanding during a mission. Maybe Rhodey made a decision that put Tony in danger without realizing it at first, and later realized his mistake. For example, if Rhodey called for backup in a situation where it attracted more enemies towards Tony. Another reason might be something related to their personal relationship outside of the hero stuff. Perhaps Rhodey said something unkind about Tony's new technology, not knowing how much effort Tony had put into it.
Tony might be initially skeptical. He's been through a lot and has trust issues sometimes. So, he might not immediately accept Rhodey's apology. For example, he could give Rhodey a cold look and say something like 'We'll see if you really mean it.'