Gardening against any wall is always a bit of a challenge--I have southern and western facing walls of off-white that reflect copious sunlight into my southern and western gardens. Brick is also a challenge in that it retains heat in and of itself, keeping nighttime warmer than it otherwise would be (even on overcast days as there's still radiation reaching the wall).

Most plants won't object, per se, but you're going to notice that you can't grow anything that prefers cold weather or anything other than full sun under conditions like those (presuming the brick wall is actually in relatively sunny conditions, as my southern and western face are). Red-colored or dark brick won't increase sunlight's intensity too much, but will hold and re-radiate a boat ton of heat. Paler brick will reflect a lot of light but doesn't hold as much heat due to bouncing the radiation away.

With tomatoes, I might suggest varieties known to do well in smaller containers, and watch for splitting under conditions like this: https://www.thespruce.com/why-do-tomatoes-split-2540002#:~:text=Tomatoes%20split%20due%20to%20fluctuations,in%20the%20tomatoes%20cracking. I will say that tomatoes generally grow better when ground planted, but I've successfully grown smaller varieties in pots. Never let anybody tell you something is impossible. It's usually not, but results may be...disappointing. If you're willing to let it be a lesson, feel free to try it. However, that brick wall will present a challenge with proper watering.

Eggplant are durable, heat-loving, and not going to present much of an issue. My own flourish on the southern face of my house right up to the wall, growing happily until well after frost due to the protection offered by the radiating heat from the wall. Again, I'd choose smaller cultivars appropriate for 5-gallon buckets and mind the watering, but you should be fine with these.

I'm not familiar with cucumbers, but a bit of spot research indicates that they won't have much issue with this as long as you can keep them watered. There are numerous varieties that look to grow beautifully in containers, but if somebody else chimes in, I'd listen to them.

And as always, experiment. And have fun with it, you have enough space to play around a bit! https://www.lifeisjustducky.com/hot-weather-vegetables/

In Chicago, where you shouldn't get extreme temperatures, I'd say it is nothing to worry about. If anything, the brick wall will keep things a little warmer on cool nights, which is more important for containers than for in-ground plants. Tomatoes, eggplant, and cukes all love sun, so unless you have a heat problem, don't even think about shade.

I'm in the NW Chicago suburbs, a southern exposure, and 1 bed that is against my brick house. I've found it is about a full zone ahead of the rest of my beds. Garlic is ready 3-4 weeks earlier than planted elsewhere. I've planted zucchini, and tomatoes there with much success, but surprisingly, my peppers wilted quite a bit when not given a bit of shade. I do plant in the ground, not containers, which will get even warmer. You might need to water quite a bit, but I see no reason not to grow there. Like morpheus, my tomatoes survived many frosts in that sheltered, warm location. :)

Worse comes to worse if you have a heat drought situation, mist them a bit. The evaporation will cool them. Don't do it if the water is likely to sit on the leaves for a long while.