Richard told Jacob he never wanted to die. This isn't limited to ageing. Richard will never die. In any instance where Richard would have died, something has happened to stop it. Everyone is assuming the dynamite didn't explode because Jack was there, but that is incorrect. Had Jack been alone, it would have gone off; it only did not because Richard was present. Richard believes he can be killed, but he is wrong.
But in the finale it was revealed that Richard was now ageing again. If he begins to age, then he certainly will be able to die another way.
Jacob's gone, his deal with Richard is now null and void: without Jacob's power, he's already ageing, and he will die. The Island's done with him, after all, and we all know how that turns out. Besides, some of the reasons for him not wanting to die (his guilt over Isabella's death) are gone: nothing now, not even himself, can prevent him from dying... and reuniting with Isabella.
Richard is still immortal after leaving the Island. He was to only main character not shown in the "flash-sideways timeline", and therefore hasn't passed on. Even minor characters, like Dogen, had a part in this sideways timeline.
It's more likely that in Richard's flash-sideways, he was either killed when the Island sank, or never arrived there in the first place, and died in the late 1800's-early 1900's as a normal man.
Christian told Jack that the most important time in his life was that he spent with those from the flight, which is why they all moved on together - for Richard, this was probably his time with Isabella, so his flash sideways is more likely to be in that time.
What's more likely is the fact that Richard, just like Eko, accepted his death and had no more connections in the world, so he just moved on upon death.
It was the Island that gave Richard the ability to not age. When the Island's cap was lifted, all of these "magical effects" wore off on everyone, including the Man in Black. That is the precise moment when Richard showed a sign of ageing (a piece of white hair on his head); however, the Island's cap didn't stay off for long, after it was put back, Richard again became immortal, the main reason why he didn't appear at the church. Jack's father quoted "We all die sometime", but it seems like Richard never died at all.
Hair doesn't just turn white instantly it takes time for it to happen. At the very least a few days would have had to have passed for one of his hairs to start turning grey, which would be consistent with the timeline of Jacob dying. As for why he didn't show up in the Church, Eko wasn't there either yet he's clearly dead. It's because everyone in the church had the most important time of their lives with each other, while Richard didn't. Richard would have moved on with Isabella, which in that world would have taken place in the 19th century. It's partially a world built on what the people in it wanted most, so in Richard's case he would have wanted to stay with his wife.
He is beyond good and evil. His interest is in protecting the Island and that's all he cares about. He will gladly save everyone on the Island if it means saving the Island itself and he would gladly kill everyone on the Island if it protected the Island. He is willing to work for people without morals provided they work towards protecting the Island. Richard didn't turn against Charles and Ben because they became evil. He did so long after that. He began moving against them once they took the Island and its rules for granted. Richard shouldn't be viewed through the lens of good or evil. Ben, Charles and Locke all have their agendas. So does Richard. He has been charged with finding and advising the leaders of the Island. Once that leader upsets the apple-cart and tries to go against the Island's rules then that leader must go. He has been granted the miracle of immortality to serve a purpose and he thinks that purpose is a noble one. He just does his job. A job that was given to him by Jacob. Richard for all his crimes lacks the character flaw Charles, Ben and Locke share... ego. Richard is willing to be subservient to serve the best interests of the Island.
Richard isn't just caring about the Island, he also cares for people which somehow sets him apart from the average Others. When he wants to commit suicide aboard the Black Rock he suggests Jack to leave rather than share his possible fate. That's pretty considerate of a person you otherwise think doesn't care.
While Richard will not hesitate to kill to protect the Island, he doesn't needlessly slay people.
Richard for all his immortality doesn't seem to be much of anything. He doesn't come off as all knowing, as a good leader and he certainly isn't fearless. This whole season we've seen how little Richard knows about anything. He can't communicate with Jacob, all of his insight in John Locke's past is based on things John has told him through time travel and nothing more. For all his immortality he doesn't actually know that much about what is going on. Even his immortality isn't what it appears to be. He was clearly fearful of being shot by Daniel... an immortal would be less likely to flinch. He flinched because his life was in danger - he can be killed. Richard has survived as long as he is because he isn't a leader. He's the perfect follower. He's a flunky, a sidekick, a lackey, whatever you want to call it. He doesn't take chances. The Island has given him the task to follow the leader and he does so. He can't regularly speak to Jacob. He can only find and aid the leaders who can. Richard survives because he's the Island's perfect little stooge. He does whatever the Island wants and that's all he does because he's too weak to be his own man and lacks the vision or ambition to do anything special.
Because Richard has immortality from Jacob, if he did anything to betray his leaders, he may start to age again.
"Dr. Linus" implies that Richard has sought death for many years, so that seems an unlikely reason.
Richard trusts Locke 100%, due to his connection to the Island. The person Richard doesn't trust is Ben: "What's he here?" he said, and he wants to know how Locke really died, suspecting Ben. He was testing Ben with the "I think he's going to be trouble," and Ben can't resist making an ally over a common enemy and blurts out "why do you think I tried to kill him?" If Richard thinks Locke is trouble, he means it in good nature, for he seems fully intent on listening to him.
Told the Others about the Man in Black
We saw in "The Cost Of Living" that the Others burn their dead during funerals. They know what happens to a body that's left unburied on the Island. Someone had to tell them about it, and since most of them are not in contact with Jacob, it had to be Richard.