Is this how to clean a fish tank?

That sounds fine. I fill my tank up to just below the rim that holds the hood and light. I don't think there is a correct answer to this. For the filter cartridge only replace them once they are falling apart. There is no need to replace them every month or whatever the company says. They only do that to make money. During your weekly water changes remove them and get all the gunk out of them and then back in the filter. Use the old water not tap water.