You shouldn't need to download Battlefield 4 again, if you already have it installed. If you removed it, you will need to download it again, of course. With the downloadable content, you can download this by opening Origin, going to My Games, right click Battlefield 4, and select View Game Details. From that page, you will need to scroll down until you see the DLC. Right click each DLC, and you will see the option to download it.
There are 3 DLCs that are not associated with Premium, and are actually free. You will, however, need to complete a "purchase" with each one, but as they are free you won't be charged. I'll go ahead and link those below.
