Where are the Transmission Solenoid and Control Board located?

They are inside the transmission attached to the valve body under the access cover. You need to drain the transmission, remove the cover and you will see the solenoids where they mount.

100 percent sure. The solenoids are mounted to the valve body that is inside the transmission. They move the shuttles in the valve body to change the fluid flow and pressures that make the system operate. That valve body looks like the attached and is under the cover on the transmission. Your car uses a 4T40 transaxle and the valve body is under the side cover. You need to drain the fluid, remove the left side axle and then remove the cover to get to the valve body where the solenoids are. Generally, most information on that vehicle also assumes you have removed the transmission first as there isn't enough room to get the side cover off in most applications that use that transaxle.

This is a tear down of that transmission:
https://www.youtube.com/watch?v=2WzF1q3hZHs

at around the 4-minute mark you will see the side cover come off and the solenoids under it. Notice the hole with the stub shaft on the right side of the image? That shaft is where the left side drive axle inner tri-pot joint goes. You can also see how deep the cover is, and how far it needs to some off to get to the solenoids.

I pull the pan off and generally plan on changing fluid and filter whenever I do transmission repairs. That gives the best hope for the repairs normally. In this case you want the fluid out of it because of needing to pull the axle to remove the cover.