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About ten gallons a week for every inch of trunk in its first year, poured slowly at the trunk all at once rather than a little each day. Half that for the next couple of years while it establishes.
Yes. With your location, the rain that fell there in the last two weeks comes off the amount, from PRISM gauge data. It can’t see a sprinkler or a roofline, so a tree under an overhang still wants the full amount.
Match it to the trunk: a 24-inch mat for a trunk under an inch, 36-inch for one to two inches, 48-inch for two to three. Past about three inches the roots reach beyond any mat, so water out at the drip line instead.