My question is whether or not one can apply an oil to the bow before it is fully tillered?
Yes, you can apply oil at any time. That's what I do. Sometimes it will be a while between roughing out and tillering, so the oil helps to prevent the stave from dying out too fast and checking. You can also use shellac or any other finish. The thinner the finish, the easier it will be to remove it when tillering, obviously.
Would a coat or two of this inhibit wood removal on the belly side of the bow?
No.
Also, would it affect the bow's flexibility at all?
No.
Does cutting nocks from the sides into the back of the bow significantly weaken the bow tips from your guys' experience?
Yes, if the neck (the space between side nocks) is very narrow.
Should I just cut nocks into the sides, or am I good to cut it the whole way round?
Never cut a nock all the way around without an overlay to protect the back.