The tenth stage of the "Van Kanigem" tournament.

Is there a chance to see a hero who escaped earlier in the week appear in the list of available heroes on the last day of the week?

If it's an enemy hero, then yes. But if it's your own hero, I can't recall such a thing happening, although I won't definitively say the opposite.

I was thinking of signing up for the tournament and submitting at least some results.
I spent a lot of time replaying and trying to improve the situation.

And in the end - I couldn't do it.

Something tells me you're not being entirely honest. I don't believe that vbn couldn't complete the map, especially since it's a relatively simple one. Laziness or lack of time, that's understandable. But otherwise...