So, I'm in chapter one, having to deal with the Nekker contract. I entered the gave, and already killed a bunch of Nekkers, at which point I get an update to the quest, that Geralt noticed Nekker tunnels and it'd be a good idea to destroy the entrances.

I didn't see any Nekker tunnels let alone entrances myself; and the quest tracking doesn't produce that convenient yellow arrow. Any idea where to look, and what such a tunnel entrance looks like?

Also, I've got several mutagens, and the manual says to go to meditation/character, find an ability with a mutagen slot, and then use it. So what exactly does a mutagen slot looks like, because I've been going over the ability trees, and don't notice any mutagen slots, nor any difference between the different ability circle. Can anyone describe what this mutagen slot looks like, and where I can find them?

Only a couple of abilities towards the end of each tree have mutagens slots. They have a little empty circle on them. But you won't spot the mutagen slots on an ability before you take that ability.

The nekker's nests look like round piles of branches on the gorund. Your medallion will highlight them, press Z to do that.

I've attached a map with legend i made for myself, but be warned, it may spoil some stuff for you because it marks a few things beside the nekker's and endrega's nests, like caves and other stuff.

If you don't want to leave it to chance on your first play, look at this post:

http://www.gog.com/en/forum/the_witcher_2/the_nearly_complete_mutagen_guide

So, I don't see the map as very helpful, it's the location at the overworld, I'm inside one of the Nekker caves.

I can use z to see red patches on the cave floors, but I have no idea how to collapse them. Striking at it doesn't work, Aard and Igni don't work, I even try Yrden since it's actually placed on the ground; but nothing destroys them. The amount of Nekker tunnel entrances destroyed don't go up; it stays at 0 out of 4. The cave now is devoid of Nekkers though, I killed them all.

The nekkers nest are not on the caves, they're on the forest.

You need Grapeshot bombs to destroy the nekkers nests, you can buy the formula to make them from Cedric

Those red patches you're seeing on the cave when using the medallion are either blood or puddles of water.

Those entrances are at totally different place. I too was looking for them in the cave for long.