A Shadowdancer isn't simply hiding: she's using a Supernatural ability to not be seen while not having anything to hide behind – she's not actually in the shadow, she remains in plain sight but unseen. True Seeing will work on her.
A Ranger is simply hiding. His Extraordinary ability allows him to disappear into natural terrain while being observed, but it's a mundane hiding-in-the-grass he's doing. True Seeing won't work on him.
In a fictional sense, this should be sufficient. The Shadowdancer is using magic to conceal herself, while the ranger is using mundane skill. True Seeing penetrates magic to see things as they actually are and will show that the Shadowdancer is actually standing in plain sight in a shadow that has been magically moved/altered/detached.
Rules-wise, a bit more work is probably necessary. The description of True Seeing doesn't list anything that seems to cover this case, and an easy answer is simply that if it doesn't say it covers it, then it doesn't apply. However, this is a simple proof that it applies to the Shadowdancer:
- True Seeing "confer[s] on the subject the ability to see all things as they actually are."
- The two lists of things True Seeing are divided into magical and non-magical effects. The magical list is things it works on, the non-magical is things it doesn't work on.
- "Supernatural abilities are magical"
- True Seeing allows the subject to "sees the true form of polymorphed, changed, or transmuted things"
- There is no way to interpret a Shadowdancer's Hide In Plain Sight without it being a magical change.
- From all of the above, True Seeing should see a Shadowdancer using HIPS.
Creating a diversion to hide
While it's mentioned as part of both the skills Bluff and Stealth, creating a diversion is detailed under the Influence skill (a combination of Bluff, Diplomacy, and Intimidate) in Pathfinder Unchained (released about 5 years after the Pathfinder Core Rulebook). To create a diversion to hide, you take a standard action, "attempt[ing] an Influence [i.e. Bluff] check against the viewer’s opposed [S]ense [M]otive [check]. If you succeed, you can attempt a Stealth check. When applicable, use the same modifiers from the lie function."
The inquisitor archetype heretic when using the supernatural ability judgment can opt for the escape judgment to grant the inquisitor the ability to take a move action (instead of a standard action) to create a diversion to hide upon making a successful attack. This lets the inquisitor, essentially, stab then hide.
(From an optimization perspective, this is acceptable at low levels, but it'll lose its luster at higher levels when full attacks are necessary to pull your weight. Further, picking the escape judgment typically means forgoing all the other awesome judgments the inquisitor could've picked instead! And the issue remains that the inquisitor still needs to end her movement behind cover or in concealment to have stealth and those conditions must be within 15 ft. of her unless she can afford suffering some hefty penalties. Also, if she has the supernatural ability hide in plain sight, that ability is just super better than this one.)
Becoming invisible as a spell-like ability
The complete text of the inquisitor's clandestine inquisition's granted power disappear, a spell-like ability, says, "You can become invisible as per the spell as a standard action. The invisibility lasts for 1 round per inquisitor level or until you attack. You can use this ability a number of times per day equal to 3 + your Wisdom modifier." Typically, a creature can only take 1 standard action per round. Thus a normal creature that takes the standard action to activate the spell-like ability disappear will be unable to also attack in the same turn. (She'll also provoke an attack of opportunity from each foe threatening her when she activates the spell-like ability disappear, by the way. Follow this link and this link to learn more about the differences between spells, spell-like abilities, and supernatural abilities.)
The special case with sniping is that after making that one ranged attack the sniper can take a move action to remain in the same place and, if the sniper's Stealth skill check to hide result (that suffers a −20 penalty) beats onlookers' Perception skill check results, the sniper need not move, the sniper's position undetected by onlookers. Snipers do this—stay in one place—because normally "Stealth immediately ends after [the sniper] make[s] an attack roll, whether or not the attack is successful." While the sniper—instead of sniping—could have just make an attack from her originally-hidden-but-revealed-upon-making-the-attack position then take a move action to move from that position, that'd mean everybody sees where she is and where she's going!
However, with the shadowdancer's supernatural ability hide in plain sight and without using the sniping rules, the sniper's position is still revealed after the attack, but, afterward, the sniper can take a normal move action (or even a 5-ft. step) in conjunction with the skill Stealth to take up a different position. (She can't stay in the same place because everybody knows she's right there because she revealed her position by making an attack!) She makes a Stealth skill check opposed by observers' Perception skill check "even while being observed." Further, "[a]s long as she is within 10 feet of an area of dim light, a shadowdancer can hide herself from view in the open without anything to actually hide behind."
This means a shadowdancer sniper in, for example, a cramped pillbox likely must use the normal sniping rules, but, if out in the open, the shadowdancer will be better off using the supernatural ability hide in plain sight.
Note: You've picked to play a minigame that, traditionally, Pathfinder doesn't play well. If you want to play a good, interesting stealth simulator, you may find Pathfinder disappointing you, and you may find the GM frustrated by your efforts to fit this square stealth peg into that round just-fight-stuff-normally-already! hole. There's a lot of confusion around the issue of stealth, and it's been the subject of long debates, frequent animosity, and at least a few official revisions. If everyone at the table objects to this particular playstyle, keep in mind for your next character that the game is a much more robust magic simulator and smacking-things-with-swords simulator.
Best Answer
1. How does this work against creatures with darkvision considering they can see perfectly in dim light?
It works exactly the same for several reasons. Firstly the Shadowdancer isn't even ~in~ the area of dim light, they're standing in plain sight so normally anyone could see them. Secondly the shadows aren't what are hiding the shadowdancer, the shadows are the required medium for them to use their (Su) - Supernatural ability; note the text:
The shadows aren't hiding the shadowdancer, they're just allowing the shadowdancer the chance to use their supernatural ability, the shadows are like a focus for a spell.
2. How should I handle the being 10 ft near dim light?
For any general ability and/or targeting of supernatural things the character needs to be able to see (ie have line of sight) to the target/object/etc in question. So that is how I would suggest running it. If the character is standing by a 20' wall and the shadow is on the other side of the wall, it wouldn't work. If however there is a window in the wall then it would.
3. Since it specifically mentions that a shadowdancer cannot use her own shadow, does this mean she can use someone else's shadow even though there is no dim light nearby?
Yes. A shadow is a shadow is a shadow; unless it's the shadowdancers. Since the ability states they can't hide in their own shadow it's a pretty safe conclusion then that every other shadow is fair game. Otherwise why on earth are they called shadowdancers?
The actual size of the shadow becomes important then (blades of grass was mentioned in another question for 3.5) and I'd require that the shadow be of at least one size category smaller than the character.