Used to be that RAW, the sniper wasn't getting the sneak attack. Why? No good reason other than that "a legalistic reading of the rules said so." There are no end of huge threads on paizo.com going over in tortuous detail how vision and stealth and all that work in PF core, especially here and here, and the summary was "slavishly following the rules means things that make no sense." You never get sneak attack from stealth because "you can't stealth while attacking" and "it doesn't say you get sneak attack just because someone can't see you, as hidden isn't an official condition (tm)."
I would previously invoke GM privilege to implement RAI - as in Pathfinder they say clearly "the GM is the law over and above the written rules" - and make it so they get their sneak attack. Because it makes sense from a game world logic/sim point of view and you can rule that's more important than the RAW point of view. IMO the clear intent was to sneak-attack someone from Stealth. You know, "sneak," "attack," things that happen in the real world and every previous edition of D&D.
Can I Attack From Stealth?
Now, however, the Stealth rules have been errata'ed to specifically say "you can attack from stealth" which means that yes, you get the sneak attack. See the updated version on the PRD which says:
Breaking Stealth: When you start your turn using Stealth, you can leave cover or concealment and remain unobserved as long as you succeed at a Stealth check and end your turn in cover or concealment. Your Stealth immediately ends after you make an attack roll, whether or not the attack is successful (except when sniping as noted below).
Sniping: If you've already successfully used Stealth at least 10 feet from your target, you can make one ranged attack and then immediately use Stealth again. You take a –20 penalty on your Stealth check to maintain your obscured location.
So the RAW has been updated to match the RAI for whatever that's worth (apparently it's really meaningful to some, though all my rogues have been happily sneak attacking from Stealth since the year 2000...).
Does A Stealthed Attack Enable Sneak Attack?
Yes, if you're stealthed, your attacks are sneak attacks.
Jason Buhlman states the intent clearly on the Paizo forums:
For simplicities sake, it should be assumed that those making Perception checks get to do so at the most favorable point during the movement of a character using Stealth, to avoid making checks every time the condition changes. Technically, I think you would get a check whenever the conditions change, but that might make things overly complicated during play.
Creatures are denied their Dexterity bonus to AC "if they cannot react to a blow" (CR pg 179 under AC). It was our intent that if you are unaware of a threat, you cannot react to a blow. I think we probably should have spelled this out a wee bit clearer, but space in the Stealth description was extraordinarily tight and ever word was at a premium. That said, I think these changes clear up the situation immensely (compared to where they were.. which was nebulous at best).
They didn't bother changing the RAW because most people use common sense and play it that way. Stealthed = sneak, etc.
RAW + Pathfinder = Sad Panda
This is why, whether you like this or not, a pure RAW approach to Pathfinder is always going to be frustrating; the devs explicitly don't bother to clean up RAW when RAI and/or common sense is clear. It's not a priority of theirs and I for one am pretty happy about that - they spend their intellectual capital making new interesting fun content instead of crafting rules and just retreading the same content year after year like WotC did with 3.5 (Return to the Return to the 1e Module, anyone?).
No, Blind-Fight does not allow you to sneak attack a target in dim light.
Sneak attack says (emphasis mine):
The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with concealment.
In order to perform a sneak attack on a target with concealment, then, you must have an ability that negates the concealment. Blind-Fight does not do this:
Blind-Fight (Combat)
Benefit: In melee, every time you miss because of concealment (see Combat), you can reroll your miss chance percentile roll one time to see if you actually hit. […]
Blind-Fight doesn't negate or remove concealment, it only gives you another chance to connect when you miss because of concealment. Fictionally, Blind-Fight doesn't represent being able to see better; rather, it represents having tuned your other senses, your focus of attention, and your knowledge of fighting toward being able to predict where your opponent is going to be even when you can't see them. Since sneak attack doesn't simply need you to know where your opponent is, but has the tougher requirement that you can see them well and that they not have any concealment, Blind-Sight is doesn't help meet the requirements.
Low-light vision can be of some help. Low-light vision allows you to see twice as far as a normal human in each type of light condition, so you can be twice as far from the light source before your target gets the concealment of dim lighting. But once low-light vision's benefit is factored in and it's found that the target does have dim light concealment from the rogue, low-light vision does nothing more for our hypothetical rogue – it doesn't make dim light any less concealing.
Blindsight is a monster ability that represents echolocation or being able to sense via vibrations. Blindsight would negate concealment due to lighting conditions, allowing a rogue to sneak attack, but how a rogue is going to acquire blindsight is a bit of a trick.
Best Answer
Here's a somewhat similar question with a relevant answer.
How does the lighting effect the dice roll?
How does vision type impact the roll when its not full day light?
That depends on how dark it is, and what kind of vision they have. Here's the rules for vision and lighting:
There would be a -4 penalty if you're in darkness, unless they have darkvision. There isn't a penalty in dim light. True darkness is less common than you'd expect at the ranges you're talking about, as someone in the party likely has a light source (unless they all have darkvision).
Low-light vision increases their light range so that they can use a light source that's farther away for dim light. There's a chart in the linked rule that has more details.
Note that if you're attacking someone in dim light or darkness and you don't have darkvision, you can't Sneak Attack because the target has concealment as well. From the Sneak Attack class feature:
Do his friends get to roll to see me and warn him somehow during my approach?
They could get to roll Perception to see you if they're in a position to do so. They do not get to warn him or take any action as this is all happening on your turn, unless they somehow have a way to act on your turn (such as a Ready Action). Technically speaking they can speak on your turn, but I can't remember any DM who ever allowed that as a defense against stealth attacks. The target can't react as it's not their turn, and they still can't tell where you're coming from as they failed to notice you. Knowing there's someone somewhere in the area who might attack doesn't negate the surprise of an attack when it actually comes. (If I did, "I always expect an attack" would basically negate invisibility's surprise.)
Note that after you attack you lose Stealth anyway, so a roll from the other characters except the one you're attacking is likely a waste of time.
If its full day light can I still do this?
This appears to be highly contentions in the Pathfinder world, but as far as I can tell, no. Here's the Stealth rule:
Now, here's the problem (again from the vision and lighting rules):
Bright light means you're not in cover or concealment (without getting it from another source). While the rule says if you started in stealth you can move and you lose it when you attack, the rules also say that you can't use the Stealth skill at all in bright light without cover. If you step into the open to attack you don't have cover, which means you can't use Stealth at all. Since the target is allowed a perception check when it's most favorable to them (see the designer note), they get to make it once you're in the open and automatically succeed.
In that case you'd need some other means to grant the conditions to use Stealth. Some options are spells such as Invisibility, Deeper Darkness, or Fog Cloud, along with feats like Hellcat Stealth.
That's the opposite of what I said before, but given the way that Perception works I think it's more correct. Once you step into bright light your Stealth doesn't work as per the light rules. That means they see you. The attacking from Stealth rules work if you're attacking at range from behind cover, or you have conditions that let you use Stealth.