Most of the time, the clicking and popping sound you hear on your Mazda Protege when backing up, going over a bump, turning, etc. is caused by failure of the "permanent lubricated" suspension parts. (whoever thought that up should be put in the looney bin).
The suspension noises you hear can be quickly, easily, and cheaply solved. I won't go into the actual names because it could be any or all of them.
If the suspension part is too far worn out, this may not work but it is worth a try in most cases.
You can purchase a grease gun needle at any parts store for about $5.00.
The needle attaches to your grease gun end fitting.
locate the rubber grease reservoirs (the black rubber part that looks like a small cone with the attachment part coming out of the top) on the suspension part. Inspect the rubber to see if it is still in good shape. It the rubber looks good, gently push the needle into the rubber at the bottom making sure you get into the rubber cone center, then using hand grease gun (not the pressurized kind) inject grease into the fitting by pumping the handle until it swells up. Do not burst the rubber with too much. I like to use the mini grease gun for this. Gently pull out the needle.
After a short time of driving you should find you have no more sounds.
Basically what you are doing is making your own grease fitting to add grease to the parts which is what they are crying for.
The rubber seals itself back and grease coming out is not a problem.
You can repeat the procedure if needed years later but use a different place in the rubber to inject.
This also keeps those parts from wearing out.
I actually own a Protege, work on it myself, and I do not put anything here unless I have tried it myself on my car with good results. My grandfather was a senior mechanic supervisor for a fleet and started teaching me to work on cars when I was 12 years old. I have restored many types of cars.
Good luck!
It works.