Kobo can only offer free books when the author authorizes them to, or if they are in the public domain.
That being said, here's some suggestions to get free books for teens:
Leave the search field in the top right hand corner blank, then click go.
Under refine your search (left hand side) click "kids and teens".
If you want to refine it by language, click a language (e.g. english).
If you want to read fiction (or non-fiction), click it (e.g. fiction).
Under filter, select free.
It gives over 1000 results using the above examples.
I also did sort by rating to put shove the trashy stuff towards the end.
It would be nice if you could filter by publication date (if you really don't like the classics) and if you could just choose teens, but I guess that's a future project for Kobo. Oh, if you really don't want classics, ignore anything with the word Gutenberg under the rating since most of those books will be classics.