How to breed the Amber dragon

Yes, the breeding time is always the same as hatching time for all dragons, rare dragons included. This means you can check your breeding time to know what dragon you're going to get; you're getting a Tree Dragon in this case.

You can verify the hatch/breeding time for any dragon with the Wiki's Dragon Reference Chart to check which kind of dragon you might be expecting. Alternately you can just look in the store in-game. Look for dragons matching some/all of the elements of the Parents (combined) that have the same hatch time as your remaining Breeding time.

Note that the upgraded breeding cave/island reduce your breeding time by 20%, but the incubation time will remain the same.

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.