Some good questions here! I tend to be flexible in my canon interpretations based on what the story calls for, though after some reflection I guess I've pretty much always treated the food question the same across my stories.
Canon has seemed to do its best to pretend like it never mentioned mundane animals (though like NonAnalogue said, mentions absolutely were made), but there are very clearly plants (loads and loads of references, up to and including things like farfetch'd's leek), viruses explicitly exist (pokérus), and I'm way too lazy to look, but I bet there's been some mention of known bacterial illnesses in there, too. And there are mushrooms, given paras/parasect. So we have confirmed representatives of almost all the domains/kingdoms of life (even ignoring early installment weirdness, you still have mundane animals in humans!), and I'm supposed to think that there just aren't any animals (besides humans)? When pokémon, as far as we can tell, haven't even colonized a fraction of the niches that would open up as a result? Nah, man. Mice shooting lightning bolts out of their faces I'll accept, but I draw the line at ecology that doesn't make a lick of sense!
So animals exist, they're both wild and domesticated. The food chain functions more or less as normal. The pokémon world is advanced enough to have meat substitutes available for people that desire them. Nevertheless, humans do eat pokémon, and pokémon do eat pokémon. It's just that pokémon don't play a major role in their diets. It really doesn't make sense to go after them on a regular basis when there are so few of them relative to things like rabbits and when they are far, far harder to subdue than things like rabbits. Pokémon generally have a better shot at killing other pokémon than humans have for the vast majority of history, so they're also more likely to eat each other than humans are to eat them. Humans are more likely to scavenge dead pokémon than actively hunt them, and when there's hunting involved it's often for some sort of ritual purpose, rather than a common thing.
PMD is interesting to me because it usually has to make at least some nod at a dichotomy between pokémon who hang out in towns and build cute huts and the ones that jump you in dungeons. Are they fundamentally different? Is this just some weird cultural thing? Are dungeon 'mons not even real pokémon at all? I've seen all kinds of different answers to this question, and where the author goes with it can really color the fic.
I still think mundane animals exist in the PMD world! Because otherwise nothing makes sense! But town-pokémon don't eat other town-pokémon here. They can survive on berries and squirrels, it's fine. However, mundane animals don't last long in mystery dungeons, and the pokémon there are trapped by what the town pokémon call the "dungeon curse," a strange delirium that turns them feral and essentially non-sapient. They will attack, kill, and eat the unwary mon that wanders into the dungeon (as well as each other), which is why you really need to be rescued if you end up in a dungeon without the proper equipment.
Windskull mentioned Fledglings, and I've got to throw a shout-out out there for the worldbuilding surrounding the food in that story. In particular I love how gummis are special magical food items generated as part of the dungeon-weirdness that will provide nourishment even for strictly carnivorous pokémon. A cool way to sidestep pokémon eating each other (though as it happens, that can occur, too) that works well with the magical nature of mystery dungeon and is a bit less handwavy than "all pokémon can survive on berries now, yes even the crocodile/cat/shark ones."