For example: his hair is grey but, what I get from the whole movie, is that he is actually much younger than he appears to be. Does he have the same sickness as J.F. Sebastian?
Roy Batty was an artificial genetically-engineered being (as explained in the opening text), and these artificial beings (replicants) had been engineered to have a four year lifespan in order to prevent them from having time to develop too many of their own "emotional responses". He was approaching the end of that life (as were his companions), which is why he had come to Earth to talk to Tyrell. And given that we actually see him die without any apparent injury at the end of the film, we can presume he was just slightly under four years old when we first saw him. From the transcript here:
Deckard: [funny look]. [pause] What's this?
Bryant: Nexus 6. Roy Batty. Incept date 2016. Combat model. Optimum self-sufficiency. Probably the leader. This is Zhora. She's trained for an off-world kick-murder squad. Talk about beauty and the beast, she's both. The fourth skin job is Pris. A basic pleasure model. The standard item for military clubs in the outer colonies. They were designed to copy human beings in every way except their emotions. The designers reckoned that after a few years they might develop their own emotional responses. You know, hate, love, fear, anger, envy. So they built in a fail-safe device.
Deckard: Which is what?
Bryant: Four year life span.
The fact that Batty came to Earth to try to have the Tyrell Corporation extend his life span was indicated by his dialogue with Tyrell:
Tyrell: I'm surprised you didn't come here sooner.
Roy: It's not an easy thing to meet your maker.
Tyrell: And what can he do for you?
Roy: Can the maker repair what he makes.
Tyrell: Would you like to be modified?
Roy: Stay here. -- I had in mind something a little more radical.
Tyrell: What-- What seems to be the problem?
Tyrell: Death. Well, I'm afraid that's a little out of my jurisdiction, you--
Roy: I want more life, fucker.
@Mr Lister points out that his "incept date" (when he was created) was actually given in the movie as 8 January 2016, as seen in an image from this article:
The opening text indicated the film was set in November 2019 so he would have been about 3 years 10 months old.
On the other hand, J.F. Sebastian was a human who had a fictional disease called "Methuselah's syndrome" that caused him to age prematurely. They put the actor in subtle wrinkly makeup to indicate this, which the actor playing Roy Batty didn't have, so however they engineered the replicants to have four-year life spans, it presumably wasn't by giving them Methuselah's syndrome. From the transcript:
Pris: Thanks. -- How old are you?
Pris: What's your problem?
Sebastian: Methuselah's syndrome.
Pris: What's that?
Sebastian: My glands. They grow old too fast.
Pris: Is that why you're still on earth?
Sebastian: Yeah, I couldn't pass the medical. Anyway, I kind of like it here.
You can see the wrinkling around the eyes in this shot (click to enlarge):
About his hair colour, that's just the way he was designed. Maybe his appearance was based on a real person (just like his implanted memories), but that's just a guess.