If by ‘Category’ you mean a field (column), you can click on the drop-down in the column header and select ‘Delete field.’ If you mean a table, it’s the same thing – except click on the table drop-down and select ‘Delete table.’
For rearranging, Airtable typically uses drag-and-drop: Click on the thing you want to move, hold down the mouse button, and drag it to where it should go. (Sometimes you don’t click on the thing itself but on the thing that looks like the ‘6’ on 6-sided dice.)
If those miss the mark, describe in a little more detail what you need to do, and we’ll try again.