1 - If you hesitate going deep with the tomatoes, lay them sideways when you plant them. You'll still get more roots and the top 1/3 of the plant, which should be sticking up, will respond to gravity and grow vertically.

2 - Strawberries are a favorite of slugs and snails. Birds eat them, too. If a bird even makes a little hole, pillbugs and earwigs will nibble.

3 - I'm not sure why you need to remove the strawberries. If you move them to a shallow trough, you'll have to water more frequently. The amount your strawberries bear depends on the variety and when you planted them.

4 - Give you carrots and scallions room to grow, usually a couple of inches apart. Next year you may want to sow more thinnly so you don't have to pull too many.

5 - If your garden is successful, you will just need to add additional compost. You may notice deficiencies as things grow and you can correct things them. Depending on whether you bed gets sun in the fall and winter (and the temperature), you can grow peas, broccoli, cauliflower and other fall crops. Some people plant a cover crop such as clover to replenish the nitrogen in the soil

You can get information specific to your area by checking the Missouri Master Gardener website. From there you can find the group that is closest to where you live. They should have information relevant to your growing conditions.

Here is a link that might be useful: My raised bed garden

It sounds like you're off to a good start with the raised bed, but how many tomatoes and peppers are you trying to grow? A 4'x4' bed isn't very big. With lots of organic material dug in (compost, manure, etc.), you could fit 4 tomatoes OR 9-10 peppers in that amount of space. With a row of scallions, a row of carrots, and 3 strawberry plants already there, my guess is you could add 1 tomato and 2-3 peppers in the remaining space.

The issue with the strawberries is that they will send out "runners" all summer, each of which will want to root and form a baby plant 6-12" away from the mother. While this is a great way to expand your harvest in future years, it means the strawberries need room to spread out. If all you want to do is get a few berries this summer and snip all the runners, then they can stay where they are until you build them their own bed. But if you don't keep up with them, those three plants can easily turn into 12, 15, 18+ plants by fall if you allow all the runners to root.

As for your clay soil, you want to be adding compost throughout the year; the more, the better. If you don't have your own homemade compost, I would suggest digging in a few bags of purchased compost (mushroom soil, composted manure & humus, etc.) at the beginning of the growing season, then top dressing with more compost once or twice through the summer. In the fall, mulch with shredded leaves raked from your lawn (rake them into a pile and run the mower through them several times to chop them up into little pieces). Over the course of the winter, earthworms should start breaking down the leaves, which you can then incorporate into the soil in the spring, along with more compost, and start the whole cycle over again. Each year, your soil will improve, little by little. :)

(1) When I replant the tomatoes, how deep should I plant? Since I didn't prep the underlying clay, should I dig that out and add something to it (compost, e.g.,) before replanting the tomatoes?

Plant them so most all of any exposed stem is buried. Either deep holes or trench them in. More digging sure can't hurt but it would be easier to just add more compost and mix it in to the top so you are working with a good 8-10" of new. Let the worms do the work of turning it in.

(2) I've got a 2' fence flush against the bed but something is getting in and eating the strawberries. There's no obvious tracks in the soil, could it just be bugs?

As mention - slugs snails and many other possibilities. Move them to a container for the good of all issues.

(3) Do I need to move the strawberries? There's 3 plants, I'm told the yield will be low the first year, I'm considering moving them to a trough this year and then to their own bed next year.

3 plants won't give you much yield. Not even a small handful of berries. Honestly not worth planting so few plants. Put them in a pot and plan to plant many more next year in a larger container.

(4) The row of scallions and row of carrots have sprouted, I planted densely planning to thin - when should I thin and by how much at first? Growing up we didn't thin until we could at least discern which plants were doing better. I'm nowhere near that point but since I planted so densely I'd want to make sure I thin on time

Since this is such a small bed and sounds like it is heavily over-planted already if you want any carrots at all you will have to thin aggressively. Begin thinning as soon as the seedlings are large enough to ID individual plants - usually 3/4-1" tall. Do a follow up thinning when they are 2-3" tall and again until they are approx. 3" apart.

(5) I'm pretty sure this soil mix is only good for about 60-90 days and I'm not sure what I need to do then. Dig it out and replace it? Add something to it?

Not at all, you just keep mixing in more compost and nutrient supplements. You will not be able to count on this new soil for sufficient nutrients without you adding supplements. There is no active soil micro-herd yet to convert the compost to nutrient forms.

(6) Assuming our garden is successful (so far, so good, I've maintained it minimally) we plan to expand next year. What should I do with the soil this summer/fall, if anything? Raised beds again is what we'd prefer.

Just build more of the same or my personal preference is 3' wide and long as you have room for. It's a more efficient use of space and provides easier access. 2x a year additions of lots of fresh quality compost. If you can get some well-aged manure for adding in the fall - great. otherwise buy several bags of composted manure now while the garden centers have them and add them in the fall.

Good luck with your garden.

Dave