You say:

The monsters have always been there and did not just turn up one day, they evolved naturally alongside other creatures including us. Species of monsters have evolved everywhere on earth that can support life, so seas, deserts, islands, polar regions you name it. No environment is completely safe. While intelligence varies greatly just like the real world, many species have displayed decent intelligence and problem solving, sometimes even use of makeshift tools.

If humans evolved alongside of them, well...the ones that are left are the survivors. And the survivors will have characteristics that allow them to be more likely to survive. This means that you're going to have monster hunters.

You have basically built a world in which adventurers are key to survival. Not everyone will be one, but you're going to have to have a lot of badasses.

Your mistake here is thinking that the economy won't be based on monsters. Which, if I know humans, it will be. This is going to be completely different world--not our world with our ideas of agriculture and commerce.

Humans solve problems, and take risks. Sure the monsters might not like it, and sure the monsters are overpowered compared to us, but we've taken down large predators in the course of human history. In a world like this, knowing how to kill monsters and having people who do that will be a matter of survival. We cooperate and we build things that make us better at killing them.

You say:

The types of monsters will be extremely varied, big, small, fast, slow, carnivorous, herbivorous etc. Most will be modified versions of real world fauna but some will be taken from mythology or created from scratch. Most are still dangerous.

Evolution is about niches. Your monsters are more dangerous than our animals in the real world, but this will mean that your humans will be more dangerous as well. Even if they do have variation, certain areas will become accustomed to the most common types and take measures to stop those.

Further, these monsters have to eat something, and there has to be an abundance of those things (animals, plant life) to sustain them. Those things will either be things humans can eat, or in the case of a specialist, things that humans can destroy to starve out the monsters.

You keep saying that some things won't work because of the variation. And simpler solutions, like tunnels (which did exist in Medieval and ancient times) people would be highly motivated to build those. You're talking about expense to build those, but you might want to re-think that because the economy is going to be richer than you might think and based on monsters. Plus, with this problem to solve, the motivation WILL be there. There wasn't much motivation to build tunnels in Medieval times and ancient times but this world has it in spades. Anyone who builds tunnels like this will have a lock on trade, and that's enough to motivate a group to want to pour their resources into it.

You've already got a lot of answers that are really great, including the wall thing, and the roof top farming is brilliant. (I would bet some of your monsters fly or can climb, so you know, any defense can be defeated by your monsters given any thought at all.)

The question is really--given a world full of monsters with any characteristics how can humans eat.

As others have said--eat the monsters.

And, your humans will be diesel as heck. Your farmers will build all kinds of things and kill a lot of creatures, even if many places take advantage of natural features and build walls.