The rested bonus does NOT apply when your character is wet and you automatically lose it until you're dry again. That includes rain, falling/jumping into a body of water or entering the Swamp biome where it's constantly raining. Annoying because it keeps ticking down but easy enough to rebuff with a 20 second sit next to a fireplace once you're in a dry area. The only way to counter this is to make as high-scoring food as you can and balance your health and stamina, particularly for the Swamp.

If you want to run a mod, Epic Loot is a good one as you can score waterproof armour and "feather fall" armour which does what it sounds like.

Regarding swarms while you're busy, logging/mining draws attention to you, hence the swarms.

Anyhoozles... as for the rest of your post.... The only answer is get good. Learn to take better notice of your surroundings before engaging or being distracted by things like logging if you're near a high-level biome that you aren't prepared for or kite mobs to a clearer area to fight.

Good luck!