Since we're talking about fiction (we are talking about fiction here, right?), we, as the creators of the fiction, can make decisions about what is possible, and what has been achieved. "A key scientist has discovered a specific type of virus that..."
Actually achieving that will be far more difficult. Your chances might be only 3 in 10,000 of having something work. But, for the sake of interesting fiction, you could say that you've achieved that 3 in 10,000.
Let's look at this in detail:
virus only active with certain conditions,
Yes, although some conditions will be more feasible/believable than other conditions. Conditions revolving around the biology of the virus, and for the virus's interactions with it's environment (possibly involving the biology of the human) may be effective.
You may also want the virus to be able to infect everybody, but to have benign effects for a certain group of people.
certain temperatures if you want to kill people in Africa but not in Greenland,
People in specific geographical coordinates (certain number ranges in the longitude and latitude scales), based on current political boundaries: no.
People who are experiencing certain environmental conditions that tend to be unique to certain geographical coordinate, like dry environments (yes), or environments with less healthy green grass (more challenging).
a virus that infects everyone but only kills when certain chemicals are present, etc) ?
In inactive virus that is then triggered: yes. This may be harder to implement, but could be feasible.
design this virus in a way that it won't mutate with time and extinct humanity?
The virus could kill itself off in 80 years or 160 years. More challenging, but could be believable.
Won't mutate: Don't count on this. Mutations are challenging to handle, and there are billions of people so there are lots of changes of mutations. Completing preventing mutation would be an aspect that is unlikely to be easy for a designing scientist to control.
Main targets would be Arab populations
What do you mean by Arab?
People who are physically located in the Middle East: possibly. Geography was mentioned above.
People who pray to Allah and do not recognize Jesus Christ as the savior of the world: no. A virus is unlikely to care about what a person's beliefs are.
People who have names like Mohamed Abdullah, Anwar, Ali, Bassim, Hadid, Hashim, Muhammad, Sadid, etc.: No. Why would a virus care whether the name reminds westerners of the Middle East?
People with somewhat darker skin than caucasians, but lighter skin than black Africans: Maybe. Strong doses of Melatonin might be an anti-body (helping the blacks to survive). Maybe whatever affects eye color or hair color might help those green-eyed blondes out there.
Males who wear turbans: maybe, if the lack of sunlight on the scalp had some affect. Could also affect baseball players who wear caps a lot.
Males who wear turbans: definitely, if turbans are made of some specific material, and the viruses really like close proximity to that material. Could also affect anyone else who might use that material, so affecting different sub-cultures could result in collateral damage.
Females who cover their faces: possibly, if a lack of exposed air/sunlight caused swelling, possibly affecting breathing.
People who don't eat pork: possibly. Pork could somehow provide a nutrient that lets the Pork Eaters survive. Expect to wipe out Muslims who follow Islamic diets that consist of only Halal meat. Expect collateral damage of Jews and Seventh Day Adventists (and probably some others, too).
People who might be living in Canada, who had a grandfather who lived in Saudi Arabia: That would be much more challenging. The virus isn't likely to care what nation your grandfather lived in. However, the virus might care about some genetic trait that is common to certain people. Then, even the move to Canada, and the separation of multiple generations, and possibly even conversion away from the religion, might not be sufficient to permit the person to survive. (Even if you had an anti-Arab slant, what would the motivation be to target such a person anyway?)
people with special needs.
Yes, you can target people with special needs. Possibly. Depending on what their needs are.
It's okay to infect non-targets but they should only cause diseases in the target group and they better be 100% sure about this.
I'm not sure that I understand the difference between "infect" and "cause diseases". Maybe you meant that it can "infect" (spread), but not cause symptoms/problems? If so, using one method to spread (to many people) and another set of characteristics to determine who gets problems, is potentially believable. Spreading and causing problems is not necessarily the same thing.
In fact, statistically, you probably have an incurable disease, or two, yourself: offhand I'm not finding the name of either, but there are a couple of diseases that are incurable, and spread through contact with human skin, including mothers affecting pre-born children, and I think the infection rates might be something like 84% of humanity for one and 79% of humanity for the other, so chances are very high that you do have one or both of them. In fact, for some time some medical experts contemplated wondered whether this was just part of the definition of humanity. However, there have been some people located without the disease, and it only does harm (not good), and spreading/infecting has been identified. If you've never heard about these, it's because healthy immune systems keep the effect of these diseases in check. So they never cause fatalities unless the person already has some other problem (being elderly or having some other disease/condition) that prevents the immune system from being in check. So these diseases don't ever cause death by themselves. (I'd be happy to update this answer if/when I come across their names again.) In fiction, you could have something that is similarly widespread, but has different effects.
Expect that any virus that will take out (kill) millions of targets will probably also take out some non-targets. Just how evil of a warlord do you want to allow this fictional character to be?
Disclaimer: I am not advocating trying to kill off all of the characteristics that are mentioned above. In fact, there is some strong evidence that I fit into multiple categories that were mentioned above. (So that is some personal incentive I have for such a weapon to not be actually deployed.) I'm only discussing from the perspective of helping fiction to be more scientifically sound.