Thanks for the comment CeJay. I really appreciate it. It made sense to me too that there would be friction between these two characters. I always imagine Caranore to be very American and Marchant to be very British. They're just very evenly matched and both have a strong opinion on how things should go. There will be more of these types of situations in the upcoming scenes and episodes.
As for the place in the timeline, this story takes place about 40 years after Archer's Enterprise. I think I mentioned that the Falcon was an old vessel of exploration build as an experiment. I haven't really gotten into telling the history of the Falcon just yet, but it was build about 20 years after the NX-01 and is also and NX ship. I promise there will be more about the history of the ship later on in the story. (I'm kind of excited about the ship and it's history and how it ties in with some of the characters on board.)
Last but not least: Thanks CeJay, for the recommendations. I'm going to check it out later today. First I have to tackle procrastination problem I'm having with my math homework.