I have to update my new phantom 3 professional.    ...http://www.dji.com/product/phantom-3-pro/info#downloads

This has 4 different updates. Do I need to do all four? Or just the newest one? Do I need to do them in any specific order?

Download the PDF instructions on how to upgrade firmware.  If I recall, you have to get 1.3x  - once you do that you can update your controller via the DJI app.  Can you jump to V1.6 from there?  Being a computer guy I would do V1.4, then V1.5, then V1.6 --- to play it safe.  Just remember to unzip the file and put it on your SD card in the root directory (no sub folder).  And once you update 1.4, delete that and put on 1.5, let 1.5 update and remove, put on 1.6.   (don't forget --- update your batteries too before moving on to each).

You may be able to just go to 1.6 - I just don't know... so to play it safe... ^^^

just the newest one

you dont need to leave your controller on do you?

My drone updated with the latest firmware but plugging my usb adapter with the sd card into the controller does nothing for the controller. It stays a constant red. Does it not need updated?

If you have 1.3 already then you can go straight to 1.6
If you have extra batteries, make sure to update them too before you delete the 1.6 BIN file. There was a battery update in the 1.5 firmware.