repairable motherboard iPhone 6? (nand desoldering problem)

Ooh...that's a lot of damage!

First things first. Desoldering the NAND should not have taken 15 minutes to come off. Either your nozzle was too small or your airflow was too low. 350C is lower than what I normally use but it should work okay. Most techs use 360-380C for MGA work on iDevices. The thing you have to remember is that you need to get the NAND up to ~220C depending on the alloy used. That means you need to push some air that is hot enough to get the IC and the board up to that temperature. Once you achieve the melting point, you can remove the IC. The NAND however is held in place with underfill, a kind epoxy so even if your solder is melted, you still have to pry the IC off the board.

You either waited too long, applied too much heat and damaged the pcb mask (what covers the traces) or the opposite, you didn't get enough heat and you pried the IC when the board isn't ready. Unfortunately, the picture isn't clear enough.

The second thing is that you should never do something new "for the first time" on a device that is valuable, has valuable data or is a customer device. The videos on Youtube make it look easy but it takes practice, lot's of it, in order to do it cleanly.

Search for videos on applying uv-curable solder mask. Depending on the damage to the board, you may be able to recover it. Also try to post a better focussed picture so that I can give you better guidance.