You have exactly four options for placing the “as-tu”:
Combien  d’enfants  entre 2-6 ans  qui y participeraient ?
I would rank them, from most to least natural: 1, (2, 3), 4! Option 1 is by far the most natural:
Combien as-tu d’enfants entre 2-6 ans qui y participeraient ?
Additional notes after your edit:
Using “tu as” instead of “as-tu” is simply more informal. Which one to use would depend on the context. In a text to a friend, I would use “tu as”. In a mailing list to lots of people, I would use “as-tu” or “avez-vous”.
“Combien tu as de…” and “Tu as combien de…” are roughly equivalent, with the latter being more informal.
To elaborate a little on why I think option 1 is natural, I guess “enfants  entre 2-6 ans  qui y participeraient” is a semantic block that would feel weird to cut. You could technically cut it at  or  but the meaning becomes much harder because bits relating to “enfants” are all over the place!
While position  would not be a problem in a sentence like “Combien d’argent as-tu ?”, here the meaning is much harder to understand with “as-tu” in the end, because the middle of the sentence is so long, so the “as-tu” ends up too far from the “combien” for the sentence to feel natural.
Why is  worst than  or ? My guess is that putting the relative subproposition (introduced by “qui”) at the end really eases the comprehension, because the sentence does not jump back to the main proposition afterwards, so that the processing of the sentence by the listener is linear. That’s my best shot at explaining what is really a gut feeling. See also the point just above.
The first one, is correct, because in a french question, you have to invert the subject and the verb, but indeed as Random said, it’s hard to understand immediately.
The second one is not perfectly correct because it starts with “Tu as … ?” which is not a correct question form.
antoine-sac’s answer is the right one I think.
But you could split it if you’d like :
Combien d’enfants as-tu ayant entre 2 et 6 ans et qui y participeraient ?
NB: Please don’t use « 2-6 ans », but « 2 et 6 ans ».