You can buy axes at the Grand Exchange in Varrock, find them lying around, or at Bob's Axes in Lumbridge.
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When you are in the dungeon, just before the fight - you can kill Zombies to get a hatchet as a random drop.
About 60 hours with dragon hatchet.
Fractite hatchets, and other fractite items, are items used specifically in Dungeoneering.
It depends on what hatchet you are using and what level of Woodcutting you are. For example if you are a higher level you will cut the object quicker than if you were a lower level. Also if you are using a hatchet such as a dragon hatchet that affects EXP gain as well.
It depends on the average hours you spend wc'ing a day.