Here is my straight and forward answer to the issue:

YES! You should use carbon for new set-ups in order to remove NH4 and color bodies (carbon loses its adsorption capacity after a couple days but it can be left in place as it soon becomes good biological filtration media).
Routinely CLEAN it like you'd do with other media. BTW rinsing bio media is always MOST important IMMEDIATELY after you've messed your tank!!!

YES! After medical treatment! Discard it soon after (couple hours).

NO! For long-term use as long as you routinely substitute part (or all) of it by fresh carbon.
Plant health will decline after introduction of fresh carbon typically during a time frame of 3 to 4 days reflecting its trace removing properties even if it is a small amount of fresh carbon relative to the water body and even with daily fertilization.
The burdon of proof? Well, many years of observation of plant health and using GAC.


Best regards,
Detlef