If you cannot see your target, you cannot cast Magic Missile
You are asking a lot of questions in this post, but I will try my best to address them.
What does it mean to see?
For this question we can reference Wikipedia, or Wiktionary(italicized text is marked by me):
Seeing: Having vision, not blind.
Vision: The sense or ability of sight, or something seen, an object perceived visually.
All points seem to lead that "seeing" an object is having a direct visual on it.
Using these definitions for the remainder of the answer, and on the subject of magic missile:
You create three glowing darts of magical force. Each dart hits a creature of your choice that you can see within range.
This implies, using the definitions above, that you cannot just know where your target is. You must have a visual on them. Let's look at Fog Cloud:
You create a 20-foot-radius sphere of fog centered on a point within range. The sphere spreads around corners, and its area is heavily obscured.
Being inside the fog implies that your vision is heavily obscured. From Adam's comment, you are under the effects of blind while you are in the fog.
A blinded creature can’t see and automatically fails any ability check that requires sight.
All of this means that you should not be able to use magic missiles in the fog, because you are blind! You cannot physically see the target, even though you may have a rough idea on where your target is.
Think of a scenario that you are behind a wall, and you know for a fact that your target is around the corner. While you know where the enemy is, you can't see them. Magic Missile requires vision. You wouldn't be able to shoot Magic Missile around the corner. What you are asking in your questions is the same thing, just substitute "Fog Cloud" with "wall".
tl;dr: RAW, you should not be able to cast Magic Missile due to the fog blinding you.
Subquestion 1: Firing from the edge of the fog
Can I cast magic missile from the edge of the fog? Would I be obscured and my enemy visible to me?
Subquestion 2: Location via Mage Hand
I cast a mage hand that grabs a hold of my enemy while I fade back into the fog. Does the mage hand now provide me with enough direction to cast magic missile and hit?
You cast mage hand, use your action to "grab" your target, and you slip back into the fog. You used up your turn. So what happens next?
Regardless on whether Mage Hand would be advantageous or not, you are still "heavily obscured" (read: blinded) by the fog.
tl;dr: Mage Hand isn't a factor for whether you can cast Magic Missile or not in the Fog Cloud.
Subquestion 3: Sensing via Bat's blindsense
If my enemy comes into the fog, could I use my bat's blindsense one round to know exactly where he is and the next round cast magic missile?
This is a tough call. Let's look at
A monster with blindsight can perceive its surroundings without relying on sight, within a specific radius.
From NautArch's reference to Crawford's ruling on Sage Advice, the wording "spot" is used instead of "see". Using this information, I don't believe even using Blindsight would allow you to cast Magic Missile.
tl;dr: RAW, you probably wouldn't be able to cast Magic Missile.
- RAW, you should not be able to cast Magic Missile whatsoever while you are in a Fog Cloud.
- You can always walk out of the fog, shoot a Magic Missile, and come back into the fog.