How do you add or change the columns (from the child table) that displayed in the parent table?

So I assume what you mean is that you were looking at a record of a parent record and there's a better child report and you want to change the columns.

No problem, just make a new report with the columns you want and I typically name it like:  

Used on Parent record 

Then edit the Form Properties for that embedded report link and change the report to your new report.  Don't put a filter on the report for anything to do with the related parent because the report link field itself will automatically do that for you.