I can't think of any reason why you cannot replace the struts in your driveway. It's a pretty straight forward job on most cars and trucks. I have no specific experience with the Tercel, but the Tercel is pretty much at the bottom of the food chain for technological advancement that would throw a wrench into the project. Usually, struts can be replaced and not affect the alignment. You will need to use the Loaner Tool desk of your local parts store to get a spring compressor. Typically, the entire strut with spring comes off, then you take the spring off of the strut and move it to the new strut, then put the whole thing back into the car. The spring will have rubber seats that fit into cups on the struts that the springs seat into. The rubber you have may be rotted, and should be replaced. The rubber seats don't cost much, if your car uses them, and you may as well get them, an upper and lower for each side, and put them in. If you do not use the seats, then you might end up with metal on metal contact that will become noisey, and could be problematic for the long life of the parts.
The bearing plate referred to when talking about the struts is at the top of the strut, where it seats inside the shock tower. As the front tires turn, the struts have to rotate, they do so on the bearing plate.
What you need to do is look for a parts diagram for your car. I use penskeparts.com to find parts for my BMW, but it does not list any Toyuota models. I assume there is a Website that lists Toyota parts and shows the relative locations. You can shop