Every attack that hits gets your Sneak Attack bonus. This includes bonus attacks from Two Weapon Fighting and its chain of feats, iterative attacks, attacks gained due to haste and similar effects, and so on.
So, yes, you roll Sneak Attack individually for every single attack that lands.
(Assuming you meet the prerequisites for Sneak Attack, of course)
If you are in a situation where you get sneak attack damage on an attack, then you get that damage.
TWF doesn't let you make attacks "simultaneously" but does allow you to make extra attacks. (Technically the TWF feat only reduces the penalties for doing so while Improved and Greater actually give you extra attacks). So, if you are flanking an enemy and successfully make both attack rolls you get to apply sneak attack damage to both attacks. Which would be weapon dice + strength (unless you are unchained rogue with dex to damage instead) + sneak attack + whatever other damage bonuses might apply.
So if you are an unchained rogue with 2 +1 daggers, 2d6 sneak attack, and a +5 dex you would deal 1d4+1 weapon damage + 5 dex + 2d6 sneak attack on each attack.
Keep in mind that the spell invisibility breaks after your first attack and you wouldn't get sneak attack on the 2nd attack, and that using stealth also breaks after the first attack so you wouldn't get sneak attack after the first attack either.
Every attack that hits gets your Sneak Attack bonus. This includes bonus attacks from Two Weapon Fighting and its chain of feats, iterative attacks, attacks gained due to haste and similar effects, and so on.
So, yes, you roll Sneak Attack individually for every single attack that lands.
(Assuming you meet the prerequisites for Sneak Attack, of course)
Generally, yes. If any of your attacks score Sneak Attack Damage, then they all do.
I can think of an exception. If you are getting your SAD only through Invisibility and not Greater Invisibility, then only your first attack gets Sneak Attack Damage. After that, your Invisibility ends, your opponent gets his Dex Bonus to AC back, and no more SAD for you.
Eh disagreed, the most common methods of getting sneak attack early on are stealth and the Invisibility spell (not Greater). Those will both only allow one sneak attack before they're broken and no longer qualify you for sneak attack. Classes with sneak attack then spend the rest of their feats/class abilities/game trying to set up scenarios under which they will qualify for sneak attack on every attack in a round.
Theoretically the easiest way is flanking. However, in practice it doesn't seem to work that well, at least in my experience.
You need to get both attacks to land at once to get the sneak attack damage on both, or just get Greater Invisibility.
For simultaneously attacking with both hands, use Dual Strike.
In the Weapon Masters Handbook (p. 9), you can take Weapon Tricks for Two Weapon Fighting to get Dual Strike. The prerequisites are steep though: Double-Slice (requiring Two Weapon Fighting), and Improved Vital Strike (requiring Vital Strike). IVS has a requirement of +11 BAB (which for a Rogue would typically mean level 15).
Vital Strike says you only get one attack/round, but this feat Dual Strike has you strike with both hands. It is unclear for both RAW + RAI if you are allowed to get the extra VS + IVS dice applied on the attacks at all (or if those feats are just extra prerequisites). But the sneak attack dice should be applied on both attacks since with this Dual Strike, they would happen simultaneously.
That's a long ways off from level 4 :(
Edit: That's for trying to solo sneak attack twice. The simple alternative noted by others is just get in flanking position, so all the attacks get sneak attack.
Dual Strike does not allow for simultaneous attacks, it allows two attacks as a standard action. So this does not change anything for being invisible, unless you're attacking in a surprise round (and thus they are flat-footed as well).
*IF* an ability allowed simultaneous attacks, then you would get the benefits of being invisible on both attacks, but you would still only get a single sneak attack, because the FAQ states simultaneous attacks (e.g. scorching ray) do not allow multiple sneak attacks.