How do they live underground and how deeply?
From what I know of our traditions and old stories, its some times mentioned that these things live underground, but there's rarely anything more specific. The forest spirits who live underground are some times called maahinen. Nice name as it has the word maa in it. Maa means ground or earth. Same kind of way as the spirit of someone who drowned is some times called vetehinen. Vesi = water.
There's so much local variations in these believes that its difficult to be exact. But in that song its quite clear that the person singing is summoning a forest spirit who lives below a tree.
The water guardian is something I'm sort of familiar with as I give offerings to it when I go fishing. I have never saw one.

In the old stories its said that the water guardian might look like a small girl sitting on a rock near water, usually its very shy and goes away before people can have a better look at it. Then the house tonttu is said to look like a small bearded man quite often. The underground dwelling forest spirits are depicted almost like Scandinavian trolls, only smaller.
Common factor in these traditions is that most of these should not be messed with or at least its good call to not anger them as that they can cause serious trouble if they want to... Make you go lost in a forest, burn down your house or things like that. But given respect and treated nicely, they'll be a very good friend to have around. All this stuff is very much like what is told about faeries of Ireland or European tradition of little people in general.