Shall I delete them from both the layout and table areas of that module or just the layout?
You can do either. Since you are new to filemaker, it's safer to just delete them from the layout. There are scripts that may refer to a field you are deleting and relationships that may use that field to link to another table. If you simply delete it from the layout, you can bring the field back or place it on a different layout in the future.
With regards to copying and pasting fields. If you are copying and pasting fields from one layout to another, that doesn't actually create a new field definition as happens if you open Manage | database and define a new field there. It simply moves the reference to that field to your new layout and this field will still reside in what could be a completely different related (or unrelated) table.
Bottom line, you should invest some time in effort in learing how filemaker works so you can better understand the consequences of these kinds of changes. There are books and tutorials you can purchase and you are always welcome to post your questions here.