I assume any attempt to copy and paste the filtered table and delete the original table will result in NA errors at my formula.
Try it and find out?

When I filter it doesn't effect the result of the formula.
Depending on the formula, it wont. Perhaps look at using 1 of the SUBTOTAL() functions for this?

Again, depending on the formulas, deleting rows in your table may or may not affect them

If you still have a problem, upload a small (clean) sample workbook (not a pic) of what you are working with, and what your expected outcome would look like.