Nathan,
The main job of a skimmer is to remove any floating debris on the surface of your pool.. These debris get caught in the basket, so that they don't get to your filter.
You can use the suction port in the skimmer to run a "suction side" cleaner.. In theory, you would only connect the cleaner to the skimmer when you want the vacuum to run.. You cannot skim and run the cleaner at the same time. Just one reason why suction cleaners, well.. Suck.
I know it is easy for me to spend your money, but I suggest that you move from 1970's technology and into this Century.. I use a robot cleaner that does not require the pump to be run at all.
Like this one...
Also skimmers do not work well unless your skimmer has a "Weir" door.. In the mouth of your skimmer, between the pool water the skimmer basket, you should have a little door that floats up and down. My
guess is that your weir door is missing..
Thanks,
Jim R.