So for Priest of Eresh's bit, I think l they meant that Beni-Enma hadn't been summoned but EMIYA had, making him the trainer for chef boot camp.
For the latter, there was a two-week time skip between the end of Septem and the chapter preceding the camping trip. It was referenced when discussing how Gil's armor got fixed. Now, it's still not a massive amount of time but it is downtime between missions.
I didn't want to do a lot of between chapters because of Mash's condition and I wanted the one arc she isn't involved in to occur near-immediately after.
As for the constant conflict, that's part and parcel of having a deadline for 12/31/2020 (in-story). That much hasn't changed from canon, though the dates have. I'm going to have breather episodes and not-war sequences as a matter of course, but after a chapter or three I get restless because the story drags.