I'm gonna give my opinion one at a time. I'm not trying to sound rude, but that's just how my opinions sound. Criticism helps people learn.
1. Starter is chosen at random
This one is pretty alright. I don't have anything to say about this one.
2. You must catch one Pokemon per route, you have multiple tries, and you must wonder trade it right after
Although, this one just straight up primarily takes one of the main Nuzlocke rules and throws it out the window. You only get one chance at your first encounter in a nuzlocke. Fail to catch it and you get nothing for that route. That rule just allows you to get free encounters you shouldn't be having because you failed to get your first encounter.
3. You can only go to each city once, except for Lumiose, and when the game requires it.
4. Lumiose is the only Pokemon Center you can heal at, but you can go to the Pokemart and use the PC
This, alongside rule 4, just feels...bothersome. Why can you only use Lumiose's Pokemon Center? Why would I want to waste my time trekking all the way back to that city just to get my PP back? Rule 4 overall just feels unnecessary and is just there for artificial difficulty increasing.
This one either requires clarity or removal entirely. Surf is required to beat the game. So what do you do? Teach the mon Surf, then when you don't need it, Fly to the move deleter and delete Surf, or fail your challenge instantly because you can't Surf? Scald is still a better move, anyway. As for no TMs, like with rule 4, it feels like an artificial difficulty spike through a handicap, and that should be an optional rule.
This one shouldn't even be here. Who uses Everstones in the first place except for breeding in Gen 6?
15. All Pokemon you have can faint twice, but when it faints a third time it is dead
This is another shining example of killing a main Nuzlocke rule. Any Pokemon that faints once is considered dead. By allowing this, you may as well just remove the nuzlocke variant concept overall because it's doubtful someone will get the same mon killed three times.
16. Dead Pokemon must be released and can't be stored in the PC to prevent the urge to cheat
This ties into the whole "Surf is required" thing. So what if all your Surf users are dead? Catch a slave or give up the locke? You should be allowed to permabox mons, because you're doubtfully going to use them aside from HMs when you have absolutely nothing you can use.
17. The only exception is your starter, if it faints, you can't use it until you beat the next gym, it can't die unless all your other pokemon die before you beat the next gym to "revive it" or all your pokemon are dead when your starter is killed
I'm not gonna beat a dead horse here. Please see my Rule 15 opinion.
One other thing. This isn't exactly the right section for a post like this. You'd get better reception from the Challenges section, more specifically, the Challenge Ideas and Discussions thread. I'll leave a link down below for you to take a gander at. Anyway, I hope you take a look and consider my opinions, and have a good day.
http://www.pokecommunity.com/showthread.php?t=220776