When you Blink you leave the normally visible area. Because the attacker doesn't see you coming when you blink back in, would you have advantage on the first attack roll?
Yes, advantage would negate disadvantage for purposes of Sneak Attack.
According to the rules on advantage and disadvantage (PHB 173, emphasis mine):
If circumstances cause a roll to have both advantage and disadvantage, you are considered to have neither of them, and you roll one d20. This is true even if multiple circumstances impose disadvantage and only one grants advantage or vice versa. In such a situation, you have neither advantage nor disadvantage.
So, for example, if you (the rogue) have both advantage and disadvantage on an attack roll against an enemy while your ally is within 5 feet of the target, you could make a Sneak Attack because you are treated as if you don't have disadvantage when making the roll. This complies with the requirements for Sneak Attack (PHB 96, emphasis mine):
Once per turn, you can deal [extra] damage to one creature you hit with an attack if you have advantage on the attack roll.... You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll.
However, if the ally were absent in that situation, you could not make a Sneak Attack because you are treated as if you don't have advantage when making the roll.
The same rationale would apply for features other than Sneak Attack that depend on either advantage or disadvantage on any attack roll, ability check, or saving throw. When any such roll is made with both advantage and disadvantage, the roll is made as if it actually has neither advantage nor disadvantage. In this case, no feature which requires advantage or disadvantage would be activated, and no feature which forbids advantage or disadvantage would be precluded.
Grapples don't involve attack rolls, so the prone and restrained conditions don't give enemies advantage on the ability check
Grapples are a special type of attack, but use an ability check in place of an attack roll. This is clear from the description of grappling in the rules - specifically, the paragraph after the one you quoted:
When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
[...] Using at least one free hand, you try to seize the target by making a grapple check instead of an attack roll: a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). [...]
This distinction is reiterated in an official ruling in the Sage Advice Compendium:
When you make a Strength (Athletics) check to grapple or shove someone, are you making an attack roll?
No. That check is an ability check, so game effects tied to attack rolls don’t apply to it. Going back to an earlier question, the hex spell could be used to diminish a grappler’s effectiveness. And if the grappler’s target is under the effect of the Dodge action, that action doesn’t inhibit the grapple, since Dodge doesn’t affect ability checks.
The prone and restrained conditions specifically refer to "attack rolls" being affected. Ability checks, such as Strength (Athletics) checks or Dexterity (Acrobatics) checks, are totally unaffected by these conditions - barring DM fiat.
The grapple option in the Player's Handbook is an attack, but it uses an ability check in place of an attack roll.
Does the sage advice on ability checks contradict this? It states that shove & grapple are not attacks?
There's no contradiction. They are unusual attacks that lack attack rolls.
And again in a 2016 tweet that references the official Sage Advice Compendium ruling:
The ruling is correct. Grapple is an odd attack that doesn't use an attack roll.
So no, a prone or restrained creature doesn't cause other creatures to have advantage on an attempt to grapple it.