Sooner or later Willy should send you a mail about new rods, that definitely helped for me. I still can't catch the really fast fish though. 'course, I'm not sure how bait works and I keep forgetting to get the skill buff from the trout soup.
Those bee swarms nearly got me a couple times. Every 5 to 10 floors is a treasure chest along with the usual elevator unlocks, so you might get lucky and get a better sword. If not, you can buy them eventually, or maybe spend copper/cash to blacksmith-up the starter sword, but that's probably a waste of resources.
I still need to plant trees. I'd guess the paths were the culprit yeah, since they seem to impede the spread of grass as well.
I'm around the start of winter now. Managed to Rank 10 Abigail's s-link, but can't quite trigger the scene. Bought the first house upgrade. Got a lot of paintings and other decorations that don't want to snap into place.