What I am seeing in the picture is a fungus on the fins, best treated with something like Proform C (a formalin/malachite green treatment), and the wound near the head appears to be a bacterial infection/ulcer in the beginning stages. Good QT water may be sufficient to heal the infection, but I would get some Tricide Neo on hand just in case. For the Tricide Neo, I prefer to mix and spray, instead of submerge the fish in solution, as it does the same thing using significantly less of the expensive product. I mix it by the quart, using 1/4 of the 1 gallon packet and when it is used up, mix a second. Treatment for the infection can be a wait and see if it improves, or go ahead and treat, your choice. Proform C is a widely used parasite treatment that will treat for all parasites except flukes, and the visible anchor worm and fish louse.
Because of the nitrites, I would add salt at the rate of 1 pound for every 100 gallons of water, (0.12%) and when water changes are done, add back water that is similarly salted.
I would recommend testing for KH, as it will tell you the stability of the pH, and with the pH values you list, I would guess your KH is low. The bio filters in the process of converting ammonia to nitrites and nitrites to nitrates, generate a lot of acid, consuming the KH which can result in a pH crash.
As you move through this, keep us posted on how things are going, and ask questions about any of the areas that have been covered. Keeping healthy koi is more about keeping healthy water than fish.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard