Put ice cubes in the disposal (about 1/2 way), run the disposal, flush out with cold water. Next put 1/2 a lemon and grind it up.
If you can see water in the trap , then the trap is holding water and you know it's working. Even if the trap is undersized (1 1/2"; instead of 2";) it would work. So the problem is probably a leaking drain pipe, the shower drain itself (the part that is connected to the shower stall) or it's leaking where the two connect. Can't fix the pipe or the drain itself without pulling the shower out. But, if you can see a rubber or lead ring around the pipe as it sticks up into the shower drain - that can be removed and a new one put in. This is a pretty common practice in concrete shower installs.
Up until 10/15 years ago we put in anti hammer tubes. The *powers that be* found that the tubes got water logged over time. So - it's no longer code. In commercial installs, spring loaded devices are used especially at the end of long runs or at the end of a series of fixtures like urinals. To replace the air in the anti hammers, drain down the water in the whole house with the faucets turned on. The idea is that when you turn the water back on it will compress the air at the highest point at the end of each pipe. That's what the *powers that be* realized that plumbers were not plumbing for - and home owners would not do.
There is no way to clean rust out of old galvanized pipes. Most DWM s have a screen where the water connects to the machine. You access it through the lower front panel. Another solution would be to put a filter on just the hot water pipe to the DWM. If you replace the pipe - use copper - and connect to the old galvanized with a dialectic union.
Find out what the freeze depth is in your area and bury the pipes below that level. Here (Seattle area) it is about 2 feet. Use schedule 40 PVC for cold water and CVPC for hot (if you are running that out also).