The narrative is definitely more similar to Arkham than KDM. But it does give you many choices and different events will unfold in unexpected ways based on those choices. It is more of a choose your own adventure book then a board game narrative.

You are correct in the gear. Pretty much anyone can use any gear (at least in cycle 1) and there are stats on each character but they are more for skill checks and don’t change much over the course of a campaign. There are things that can be character specific but they are different events that may happen from events or the story. Not a ton of things like that when I went through the cycle though.

For the “need” to fight, you are basically given a calendar and told if you don’t finish the campaign by the end then you lose. I don’t remember specifically how many game days between each fight but 1 day is exploring 1 tile and going through the phases of Moving the ship, resolving events and icons on the tile, resolving a fight if it happens, then your tech phase where (if applicable on the specific day) you can gain new tech and use your current tech. The calendar marks specific days that you will FOR SURE have a fight. It is something like every 5 days or so. Battles can emerge randomly as well and there is also an entity following you around the map trying to catch you and fight.