The following excerpts are from the Villain's fandom page on END, under the section titled 'Alvarez Empire arc'
During a fight between Zeref and Natsu the latter revealed his relationship to Natsu and the Dragon Slayer's status as E.N.D. Though Natsu refused to believe it at first he was forced to after Zeref pierced a hole through the Book of E.N.D. and Natsu ended up hurt as a result which proved the elder Dragneel's story. After Zeref revealed what really occurred in the past Natsu lost his patience and attempted to kill his brother as he was told that if Zeref died it would possibly mean his own death as well. Natsu ignored this and declared his intentions of wanting to kill Zeref only for Happy to fly away with him.
So yes, Natsu's life was tied to both Zeref and the book.
After that: (slightly abridged; emphasis mine)
A while later Mavis Vermillion managed to obtain the Book of E.N.D. She then met up with Lucy, Happy and Gray and lent them the Book.
They soon decided to open the Book and when they did Letter Magic flowed out of it; Lucy was shocked about what it said.
Lucy tried to rewrite the words in the Book but became affected by its Black Magic. Gray then helps her get through the pain and continues to rewrite the book. The book's changes affected Natsu during his fight with his brother; they gave Natsu the edge he needed to defeat Zeref.
Later, Zeref died peacefully with Mavis and due to the Book's link with Zeref it disappeared. When the Book disappeared Lucy claimed that she did all she could to help Natsu and worried that he could disappear along with the Book. However, Natsu showed up where Lucy and the others were saying the fight was over.
This explains how Natsu is able to survive post Zeref's death. We are to assume whatever Lucy edited managed to save him. It would be logical to assume that his END powers are gone since both Zeref and the book are gone, but there is no official confirmation as far as I know, and is thus debatable.
There is also a sequel called Fairy Tail 100 Years Quest that picks off from where the original series ends, though the author is not Hiro Mashima. I haven't read it, but the summaries don't suggest any usage of END powers in the chapters so far. But since the sequel exists, it could end up either way.