Dragons keep their levels, they are only visually reduced to babies. They will also level normally after being made into babies. They will never return to adult form unless you bring them back to the Fountain of Youth again.
Dragons that could breed before being returned to baby form can breed after they're baby-ified as well, so you can breed two level 4+ "babies" after using the fountain of youth.
Dragons can be made level 10+ through use of the Elemental Shrines which you start unlocking at level 18. it's entirely unrelated to the fountain of youth.
The dragon must be at least level 10 to be "baby-fied". The dragon can not be baby-fied until it has reached level 10 otherwise it is completely impossible to turn a dragon back into a youth. The dragon will looks as if it is in it's juvenile stage at 5 hours into the 12 hour process.
EDIT
With the race being put into the game this could not be a much better way to change Gold into XP. The race will always cost you 50,000 gold and the reward is random, but hitting even 1.8m in a reward out of 20 tries would average the results of breeding metal dragons listed below. However, I am going to leave the information below as well because there is nothing saying you can not breed metal dragons while running races.
Based on the data I could find, raising dragons is the best gold to xp exchange granting a 4 to 1 ratio for Earth dragons and a 2 to 1 ratio for Fire and Metal dragons.
Behold, a chart! (Created with v1.7.2 data)
The above ratios assume you are not keeping the dragon and are going to sell the dragon as soon as it hatches. It also only contains dragons that can, at this point in time, be purchased directly for gold and raised.
There may be some long game plan you could do with raising farms to raise dragon levels but there is not currently enough information available for me to crunch those numbers to see if it is more efficient to sell a higher level dragon vs the food costs to get it there.
One last note selling and buying dragons every 5 minutes is not the least tedious thing to be doing, but it does cycle through your hatchery pretty well depending on what types of dragons you are attempting to breed.
Best Answer
Since this question has languished for so long and has no less than five duplicates attached to it, I decided to throw myself into the fire and reinstall DragonVale. By signing out of GameCenter I was able to restart my park and quickly play through to this part in the tutorial.
The screen I was presented with differs from the screenshot in this question and from what I remember the first time I played the DragonVale tutorial, so it seems likely that Backflip Studios has updated the game since this question was posted.
Regardless, in the current version of DragonVale, at this point in the tutorial, you are asked to clear one specific rock, which is marked with a big green arrow. You are not asked (and cannot) clear any rock in the park. Selecting an incorrect rock results in the spade icon being disabled.
Here is a screenshot of me selecting an incorrect rock:
Here is a screenshot of me selecting the correct rock and then being able to remove it and continue on with the tutorial: