Glad the Material check worked.
For the parameters - there is no way to let users input the name of a parameter to check against a category. If you already know the category and parameter name, you can see if it has been assigned with a check like this:

This check will look for a parameter called "My Parameter" in the Walls category and fail if it that parameter isn't assigned to that category.
If you need user input for the Parameter name, you can create a check that allows that to see if it's in the model. However, you cannot filter that down to a category. That would look like this (needs some testing):

This may be way too deep, but hopefully it will help you with the Model Checker. As a rule, for the Advanced checks, the Model Checker can take "one step" deep into the Revit database. I can go to the Walls and see if they have a specific parameter because that information is in the Wall element. In the Revit database, going from the parameter to all the categories it is associated with is actually "two steps", because I have a table of parameters, but I also have a table of categories. The parameter just refers to the category table to know where it is assigned. That data isn't "inside" the parameter element.
I might have made that more confusing than I meant to. If you are not using the Revit Lookup tool (2019 installer here), I would strongly suggest downloading it and installing it. This gives you a peek into Revit as a database structure and is extremely useful when trying to build more complicated checks.