In general, the threading on shower arms and shower heads are universal, they are all the same 1/2" threading. You can pretty much install any shower arm into the threaded union that is recessed inside the wall, and you can install any shower head onto the shower arm. There are always exceptions. But just look for the 1/2" threading. Valve trim kits? In general, they should be specifically matched to the valve body that is plumbed inside the wall. If you can identify the manufacturer of the valve and the specific valve model, that will be the best way to get a new trim kit that will fit.

The Symmons valves are excellent valves, they've been around for years. But their trim kits are more functional than stylish. I don't have any broad knowledge regarding what trim kits can fit other manufacturer's valve bodies. What I've had to do on the past is to look at the dimensions on the valve and trim kit spec sheets and compare. Tedious for sure. If you have a simple valve you have more options than with a multi-function valve.

Do you know what the fixture name is? Look on the valve do you see any letters. M would be Moen, K would be Kohler, the rest they usually engrave an entire name on it. Is there another bathroom in the house, if this is an original builder home fixture, most likely they used the same brand fixtures throughout the house. Check Universal trim kits and see what multiple manufacturer valves they fit. You can get them at the Box store and bring back if they don't work. Another way is to shut the water off and take the stem out, bring it with you to the store and try to match that way. Good luck

Need bigger hammer.