At the end of Breaking Dawn they are given confirmation that Renesmee will live forever and not age past 18. They live happily for a while, Jacob just glad to be a part of Renesmee's life. Renesmee loves Jacob very much growing up, even when she wasn't aware of the imprint.
At the end of the book Nahuel, the human-vampire hybrid the Cullens have just met, states that she will probably reach complete physical maturity around seven years after birth, physically appearing to be around sixteen or seventeen years old, at which point she will stop aging and live to an unknown extent.
Although the timelines of their lifespans work out, Renesmee will ultimately outlive Jacob because she is part vampire, and while it seems endearing that Jacob would live his entire life dedicated to her, he comes across as a sad puppy dog who is begging for attention.
It's been a while since I read the book, but it was stated that while Reneesme will enjoy a much longer life thanks to her half-vampire genes, she will not live forever. It will be Jacob's aging process that will slow with hers since he “imprinted” on her.
Renesmee got married to Jacob and made Lucina her maid of honor. In Have A Purpose, Renesmee reveals that she is pregnant. She gives birth to Evan and Sarah and appointed Lucina as the godmother to her kids.
She informs the Volturi, as immortal children are not permitted to live. The Volturi reach Forks intent on killing Renesmee and the Cullens. However, the Cullen family members gather witnesses from around the world to prove that Renesmee is not an immortal child.
Jacob will live as long as he keeps phasing and he won't stop as long as Ren is alive. So technically he CAN live forever but he could also be killed by a vampire, another wolf-shifter or Ren could die by one of those and Jacob would stop phasing and die of old age.
Renesmee can survive on either blood or human food, though she prefers blood, and she does not produce venom. Her special abilities are transmitting thoughts to others by touching their skin and penetrating mental shields, the opposite abilities of each of her parents.
Twilight fans have pointed out that the sound was that of Bella's spine and/or ribs snapping, though that happened during the birth, while others believe that, while it's possible that Renesmee bit Bella at that moment, there was more of Edward's venom in Bella, so in the end, he was still the one who transformed her.
When they phase into a wolf for the first time, they stop aging. There are plenty-a-plot-holes here BUT if Jacob maintains a regularly scheduled shape shift, he can essentially stay young forever. This is a good thing because Renesmee will be Jacob's age physically in a mere few years.
Members of the Quileute wolf-pack do age if they do not phase for a long time; Jacob's body has physically grown to the equivalent of a 25-year-old in Breaking Dawn but stops aging after that. Jacob is the largest and strongest of the pack.
What would happen if Renesmee and Jacob had a baby?
Their child would be 1/4 human, 1/4 vampire and 1/2 werewolf, which would make them a threat to the Volturi. Renesmee is fertile as she is 1/2 human. The only aspect of herself that is a vampire is that she'll never age after she matures and she drinks blood.
Renesmee, however, does need to sleep. In both the books and the movies, there are instances of her parents tucking her into bed or watching as she sleeps. Unlike most new parents, however, Bella and Edward aren't constantly exhausted.
Renesmee, however, will only age for a few years before she's reached the vampire equivalent of maturity, appearing as a young woman seemingly forever. The only other human-vampire child in the franchise is said to look like a teenager and stopped aging at seven years old.
Renesmee Cullen was not a normal child. As a half-mortal half-vampire being, the Twilight baby grew rapidly and could speak seven days after she was born.
As Bella holds her, Renesmee's vampire heritage becomes apparent when she bites Bella, showing her inherited sharp teeth and natural desire for human blood.
Bree Tanner, a newborn vampire from Victoria's army in Eclipse, described her blood to be “the sweetest scent she'd ever smelled,” but why exactly was Bella's blood so special is unknown – it might be attributed to her blood being O-negative, or even to her diet.
By imprinting on Renesmee, Jacob has imbued her with protection from other werewolves in his tribe. Jacob explained to Bella that he was never actually attracted to her but to the baby, Renesmee, developing in Bella's womb, an explanation that has troubled people ever since.
Bella falls in love with Jacob in New Moon. I think it's easy to understand why this fact doesn't occur to her. Bella has only fallen in love one time, and it was a very sudden, dramatic, sweep-you-off-your-feet, change-your-world, magical, passionate, all-consuming thing (see: Twilight).
It's the sperm in the semen. Sperm are living cells. Edward is dead - his cells have been burned and crystallized by venom, as described by Stephenie Meyer herself. Therefore his sex cells (sperm) are also dead.
Jacob was initially in love with Bella, but she chose Edward and gave birth to Renesmee, a half-human, half-vampire hybrid. As part of the imprinting, Jacob will only be a brother figure to Renesmee until she comes of age, by which time she may develop romantic feelings for him, and vice versa.
Although Edward and Bella tell him that Renesmee is an orphan that they've adopted, he discovers their biological relation when he looks into her eyes (which he recognizes as his own), but decides to stick to the adoption as their public story for their safety.
