If I am interpreting your question correctly, no, you don't get to double dip.
DR does not negate sneak attack damage. The sneak attack damage is not a special effect that accompanies the attack, it is part of the
damage roll. Hope that clears it up.
Jason Bulmahn Lead Designer Paizo Publishing
...Meaning the damage is one lump sum.
The +5 hit and +5 damage (at level 20) applies to the individual attack. If you have multiple attacks (as would be expected of a 20th level slayer) then each attack also gets this bonus. This means that the +20/+15/+10/+5 you have for your attack bonus is +25/+20/+15/+10 before you add in your stat modifiers, flanking, weapons bonuses and spells. Additionally, each attack in that multiattack sequence gets a flat +5 to damage (totaling +20 damage should all attacks hit) before calculating strength bonus, weapon bonus and other magics.
One damage "roll" can contain multiple additions and dice from different sources, but it is still one damage roll. So if your slayer was using a +3 flaming greatsword and had a +4 STR bonus and 6d6 sneak attack and +5 studied target bonus, the damage roll is 2d6 (sword) + 3 + 1d6 (flaming) + 4 + 6d6 +5. When an ability intends to add a point per die, it is instead worded as e.g. "+1 per die of damage."
So you do get a +5 to hit and damage but they are not treated as separate entities. Ergo, its a one time addition to damage and to hit. Its not meant to be a boon per die being rolled. Otherwise you would have a rogue that would always hit on targets they are able to sneak attack and always do massive amounts of damage.
Remember, although not stated in the rules, the concept "damage roll" refers to the whole pack of dices rolled and it's bonuses when damage is rolled, in opposition to "single dice roll". You can see similar language in all strength damage bonus descriptions in the rules:
Strength: Temporary increases to your Strength score give you a bonus on Strength-based skill checks, melee attack rolls, and weapon damage rolls (if they rely on Strength). The bonus also applies to your Combat Maneuver Bonus (if you are Small or larger) and to your Combat Maneuver Defense.
And yet, a Greatsword (2d6, or 1d6+1d6 to damage if you prefer), only gets the strength bonus once (which is 1.5 in this case because it is a 2-handed weapon), and it doesn't matter if you apply sneak attack or a flaming effect to it, the strength bonus only applies once to the damage roll.
Source
There are a lot of different ways someone can be denied their DEX bonus to AC, so "it depends." So the first thing you need to note is that
d20PFSRD:
The rogue's attack deals extra damage anytime her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target.
You do NOT need an opponent to be flat-footed in order to sneak attack them. Now, being flat-footed does deprive you of DEX bonus to AC, so it also triggers sneak attack, but
a) flat-footed does more than just that, like prevent you from making AoOs, so read the condition and
b) there's a lot more ways of being deprived of your DEX bonus short of being flat-footed (blinded, stunned, the opponent being hidden, about a dozen feats, etc).
Confusing flat-footed with denied DEX to AC will lead you astray in many cases. When a rule says one that's what it means, and while flat-footed also means deprived of DEX to AC the converse is NOT true.
Surprise Rounds
During a surprise round, an opponent is flat-footed, and does not lose the flat-footed condition until their first action. So they may be sneak-attacked with impunity by multiple attackers, or multiple times by you if you can somehow do that in the one action a surprise round gives you.
Invisibility
Unless you have improved invisibility, with normal invisibility you become visible as soon as you attack, so the target is only denied their DEX bonus to AC for the first attack. They are NOT flat-footed, so can take attacks of opportunity if they know where you are. If they know you're there from a DC20 Perception check, I'd say it's a little ambiguous RAW-wise whether they'd get an AoO from, for example, you attacking from invis with a combat maneuver that provokes (grappling them without Improved Grapple for example) - most GMs would rule not, but be advised that invis isn't perfect and has a lot of caveats in its description.
Other
There's a lot of ways to lose DEX to AC and they're all different, and whether they persist for one attack or one round or forever is all based on the specific power.
Also see
Best Answer
Is it above the damage cap of max 10d6?
According to the entry for vampiric touch:
The cap is just a maximum that can be added by caster level.
Does it convert to temporary hitpoints?
The sneak attack damage does qualify for temporary hitpoints.
But you are still limited to the same maximum temporary hitpoints