we now know that Zeref's curse is from a god and since Natsu is supposed to kill Zeref and destroy his curse the curse of god then that means that Natsu has a god slaying magic which explains how he ate and used Zancrow god slaying flames.
further more Natsu is one of Zeref's demons which means that his magic is effective against demons and that means that Natsu is a Dragon God Devil Slayer .
Its more just Zeref himself that Natsu has to overcome, but the curse may play a part in it. Even though the curse is from a god, I'd say that its more Natsu's Etherious Power that will allow him to break the curse and kill Zeref, rather than him having God Slayer Magic as well.
I actually believe that Natsu is "nomathertheenemy slayer"
Back on topic... it is actually a very logical assumption, we still need to know how Natsu find himself under Igneel's care and his God Slaying magic might be dormant...
Now if he was made with the same idea as the devils from the book of Zeref does that mean that he is also a devil?, meaning possibily that the ultimate showdown could be between Natsu and Gray (if Natsu goes out of control?)
Well, people definitely seem to think the curse was from that ancserham god but we have no reference of ancsehram being a real being. We've never even heard of the guy until the last chapters. Its entirely plausible that zeref's curse was simply a side effect of some experiment he carried out or something and not the work of a god. Now, god's definitely exist considering there is god slayer magic but that is not proper evidence of this hypothetical ancsehram being a real thing.
This honestly doesn't make much sense. I don't know why he's being considered a Devil Slayer, since when has Devil Slayer Magic been necessary to defeat a demon. God Slayers are wielders of a very specific type of magic. Natsu doesn't utilise that type of magic. Therefore, Natsu isn't a God Slayer. It's unlikely to even be a requirement for someone to wield God Slayer Magic to defeat a god. It, like the other race-specific magics, is probably just helpful in that endeavour.
Yes Natsu is absolutely a Dragon God Demon You Name It Slayer.
Seriously though, I'm pretty sure that Erza, Gray and Lucy would be able to take care of the War God, but I have a feeling that War God is just a title. They are beings of extreme magical power, summons that require something greater than a contract to bring forth, but it doesn't mean they are invincible. I'm sure that others would've been able to take care of it.
Although the God Slayers are most likely used to fight against something like that specifically, but see what Natsu managed to do against Zancrow. He beat him by absorbing his magic. He could very well do the same to the War God itself.
On-topic, it has never been the case that one has to be a slayer type to defeat the the correspoding species. We already have Tartaros demons (who were Zeref's elites) being defeated by other mages. Also the thing about Natsu eating Zancrow's flames is quite irrelevant seeing as Zancrow was comfortably eating Natsu's flames. Being a slayer doesn't even guarantee being able to slay the being. It is helpful and more efficient against the being but it is not a sure-fire and neither does one need to be a slayer to defeat the being. If Natsu somehow turns out to be an all star Slayer, it wouldn't be because of the listed reasons.
"means that Natsu is a Dragon God Devil Slayer" ...?
Nah, correctly means that Natsu is a Troll-Based Slayer Magician. Not that it's a bad thing
I don't see the relevance of who taught the magic when it comes to how good it is. The manga has yet to actually make that point in a convincing manner. Not to mention that the other types of slayer magics we have seen seem to be every bit as effective as they are supposed to be. If there is a difference it wouldn't be at the base level. The difference as far as I can tell would be dragonification and dragon force. Well, grey was seen turning into a demon but demons turning into one might not be as effective as turning into a dragon if a demon by itself is not as powerful as a dragon. Then there is the issue of dragon force which seems to be the actual power of a dragon.