It's not horseweed. I pull that out all the time. Leaves/stems are not hairy, but have a slight sheen (I took the above picture in the rain, so ignore the shinier raindrops). Stem is square in cross-section. Leaves are opposite.

This first sentence is the answer: "If it is really hot, then watering, and spraying the leaves, every day may well be necessary." I'd simply add that you're dealing with transplant shock and that it is very normal under your current conditions for the entire tree to defoliate but to also, come back. It is entirely possible the tree may re-foliate this year even. Or, it may send most of it's energy to the rootball at this time. It's the tree's choice basically. I believe that keeping up on water will keep it alive on both top and bottom. When, or if you notice the buds dying, then expect the birch to sucker and as mentioned above, you'll need to remove any portions that do not re-foliate next spring and select new emerging growth for the style you wish for (clump or single trunk). If you have a cultivar of River Birch, then the new suckers that come up may not be be true to cultivar form but since you did not mention this, I won't assume. And this only applies for grafted trees. Trees produced from cuttings (I'd have to look River Birch propagation up to know for sure) - will produce suckers true to form. Yes, they are produced from cuttings. Dirr and Heuser (2006) confirm this. Dax Dirr, Michael A and Heuser, Charles, Jr. ÂThe Reference Manual of Woody Plant Propagation: From Seed to Tissue CultureÂ; (Second Edition 2006); Varsity Press, Inc. ISBN: 0942375092 or ISBN: 13: 978-0-942375-09-1

What a great idea for that space! You might want to peruse some sites to get a visual look at the plantings others have used (see my link below). Or just study creek beds (although your plants won't be the usual 'water' plants due to dry conditions (unless you want to lay a drip line along the banks of your stream). In real creek beds I think you'll find that there are all sizes of stones from boulders to gravel, grasses and wildflowers of different heights. It sounds like your choices will have to like a fair amount of shade. Also, I would recommend laying some thick landscape cloth in the 'creek bed' prior to adding the rocks. That way any weeds that eventually form between the rocks cannot establish very deep roots and can be more easily removed. Of course a little Roundup sprayed onto weeds might be just as easy. Here is a link that might be useful: google image pages of 'dry creek beds'

Obviously, this was a prime example of...wait for it...red herrings. You have a birch. Which is highly subject to water stress. To much, too little, it's a day that ends in y. Oh yeah, and you are in Oklahoma? End result, leaves on the ground. Consistent moisture. That's worth repeating. If the rootball was dry enough that you had to wet it down to scrape a little soil, you were far to dry for what a birch likes. In this age of the internet, I absolutely refuse to post a picture of any tree that I plant. Someone will find something wrong with it. Mulch circle too big, mulch circle to small, OMG, you even used a mulch circle? I think they are ugly blights upon the landscape. You staked that tree? You didn't stake that tree? that tree was staked wrong because...well, you supply the reason. You planted a tree that was HOW big? You planted a tree that was HOW small? Fertilizer? Another hot button topic, and spikes are a hot button subject within the topic of fertilizer. You were stepping on landmines and had no idea. And everyone has some kind of rationale to support their notions, yet when all the bs is cleared away, most of it is personal preference. Consistent moisture. fertilizer will push new growth, and everyone and their mother will have an opinion on whether or not you should. my .02...follow the recommendations of the person who is covering the warranty. Because let's face it...they didn't do too bad, and the advice is pretty mundane.