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Ive done this with a fair bit of firewood. Just take your time stacking your wood. Any that are nice straight fat logs free of limbs or knots can be tossed to the side for hand splitting later. Side Tip:If any of your blanks split out wrong or taper too much just use them over your firewood stack for a more attractive weather covering (shakes vs tarp)
If you're starting out with this type of joint, you should lookup drawboring too; it can make even a sloppy and loose joint snug and clean.
Traditional bench hooks were usually made of one piece (two cut from the same length of stock at a time), and seldom more than a few inches wide. Im glad to see someone else making wide bench hooks as I do, mine are just under 12 inches wide.
I know its because it was leftover materials you had, but MDF in a bathroom environment? Paint, many layers of paint; oil based if possible. I only use MDF for templates or jigs when I don't have anything else. I personally loathe the stuff, high humidity and it begins to degrade structurally, and if it gets wet don't bother salvaging; like a cookie soaking in milk for an hour.Good design overall. I like the doors, contemporary without looking dated. Great job.