Because Eobard killed her in the past, that event will be unchanged because Barry didn't stop it.
Eddie killed himself, so I assume all the Thawnes of the future have been wiped from existence. By all time travel movie logic lol, only an event in the past can affect the future.
Not exactly, for me. I'm sure season 1 is just a big time loop. because, if RF doesn't exist anymore, then, who will return in 2000 to kill Nora Allen ?
My guess is that when Barry returns from what will probably be Earth 2, he will find a very changed Earth, which will follow the "original timeline" (the timeline before Eobard Thawne changed it by murdering Barry's mother, if you prefer) with only one (but big) change : Barry is now the Flash (in the original timeline, he was supposed to be Flash 9 years later)
So, in this new reality :
Both Barry's parents are alive and well
The Wells are also alive (which means Tom Cavanaugh is back) and are working in Starlab to create the particule accelerator.
Because of that there is no supervillains at the time, and noone has ever heard of the Flash. Central City is a quiet city.
Season 1 will only have happened to Barry and Cisco (even if Cisco has no way to understand that his dreams are in fact a time loop in this reality)
Iris will never have grown with Barry as a brother figure.
I don't know what will happen for Cisco, Caitlin and Ronnie, but they probably won't have a great life in this timeline, if Eobard Thawne is right when he said he created a better life for them. (he said that in "the Trap") But I'm sure that Barry, during season 2, will recreate the team.
There could also be a way for Thawne/RF to be resurrected in the show. Say in future seasons there is an event that they can't deal with and they need the help of Dr.Wells/Thawne. The night he killed Nora Allen is still in continuity, since he was stuck in the past. As the finale said, he had 1 minute & 52 seconds before the wormhole closed. It closed, trapping RF in that timeline. So that event will most definitely always be in play. What's to stop The Flash from returning to that night or pre-Eddie death timeline and taking Wells/RF with him?
To me he is already reborn. For me, Eobard Thawne did a fatal mistake in giving Eddie a better life than in the "original timeline". I'm sure Eddie was meant to be Cobalt Blue. But, Eddie having a better life annihilated his jealous nature. Eobard tried to realign his destiny by showing him that Barry would marry Iris and not him, but it didn't work. He turned Eddie to a hero instead of a villain, and was then erased from the timeline. But, by being erased, all his past and future action have been erased to, realigning Eddie life with his Cobalt Blue destiny (just probably a little sooner). This "new" Eddie has, like anyone if Eobard is right, a way harder life (I wouldn't be surprised if he is now the janitor of the police station and not some kind of elite cop), will become a villain, have a son.... and then Eobard Thawne will be reborn in the future... only to someday (but for that, Eddie will have to become a villain and Barry has to make something bad to Eobard Thawne) return in 2000, being stuck, taking Well's life, creating the Flash... and being erased someday to realign the timeline !