Let's start with a bit of trivia. Mercury wasn't invented by Hugard and Braue, but by John Scarne. A lot of Hugard and Braue's work doesn't give proper crediting. I believe the Fred Braue gives credit for the move to Scarne in the Fred Braue Notebooks, Volume 3.
Reality: When you say squaring the deck, should the second fold be done in that time as well? Do you raise the deck up a little bit? I know they won't be burning your hands, but still too much movement can detract attention from what you are saying.
Whey you square up a deck you take it in end grip and pull your thumb back on the left side of the deck going from the outer left corner to the inner left corner and then usually return the deck to mechanics grip / dealing position. There really are four moves going on (fold, fold, turn, crease). The first is covered by pulling your thumb back, the second happens naturally as your thumb reaches the inner left corner, the third happens the instant you change directions of the deck (i.e. going from squaring to returning to dealing position) and the fourth happens as the deck is being returned to dealing position.
You don't need to raise up the deck (that would look unnatural for a squaring movement). For the third move, the movement is the left hand turning slightly outward and palm up. At that point, the movement is slight, is covered by your right palm and the change in direction of the deck (the bigger movement) will cover the left hand (the smaller movement).
The keys to getting a good (it will rarely be perfect) fold are: 1) having your right thumb significantly further down than your typical end grip. The outer phalanx should be below the deck; 2) having your thumb pointing straight down (my end grip usually has my right thumb slanted toward the left); and 3) having the side of your left index finger touching the deck and not the card (that also reduces the noise). If you want it to be perfect, score the back of the card along where the folds will go.
Although I've broken this down into four parts, they are all done as one motion so that the inertia of the first move naturally causes the second, which triggers the third and so on.
The Hugard and Braue handling is the one that suggests handing the deck to the spectators after doing the first and second parts of the fold. That seems to me to be better cover because there isn't the extra movement of returning the deck to dealing position. When I use this in a card to wallet routine, I show the card isn't on the top of the deck and isn't on the bottom (turning the deck face up - try this and you will understand why) and then do the fold as I hand the spectator's the deck while saying "I'm pretty sure it isn't anywhere in the deck." The handing the deck to the spectators is a really big motion that could cover palming a small elephant.
Giobbi's handling of squaring the deck will work well, but there needs to be an added level of misdirection.
Bannon's handling eliminates the need to turn the deck face up and can be done in two motions with a pause between each motion. I noticed that a version of Creased Lightning is also explained in Smoke and Mirrors (don't have that... yet). I also understand that the July 2009 issue of Magic magazine explains a similar method (in the "Expert Talk" section p. 71). That method gets a better fold than Mercury.
The other method that is out there is Tommy Wonder's (there is a great clip from an L&L video out there with his ambitious card to ring box where he does the fold). His fold gets the card into eighths - yep, I said eighths. The final fold is done in place of the third and fourth parts of the Mercury Card Fold and is similarly covered.
As for any misdirection, it needs to be a natural part of a routine. In Card College, Giobbi uses it in a routine just after a big reveal. Similarly with Tommy Wonder as part of his ambitious card. The cover is you just sitting back and watching the reaction. The best misdirection is a natural movement that has a justification within the design of the effect. I also like the handing the deck to the spectators.
You can talk and make eye contact while doing the move. It just takes practice. Tommy Wonder says it will take 50 decks to learn his variation. I suspect, that Mercury or Bannon's could be mastered with a mere 10 decks. After you have the mechanics down so that you can repeatedly do the move in a single motion, practice the move while talking - the best practice is under performance conditions.
The Mercury card fold should be covered by riffling the deck. It should just seem like you're playing with the cards by riffling with them, then on the third or fourth riffle, do the move, and cover it with another riffle afterwards. This covers the sound and actions of the mercury card fold. Another important thing to remember is to establish eye contact with the spectator, and talk to them whilst doing the move.
I really disagree with this. You are actually drawing attention to the deck. Do you really think that the spectator isn't going to think that something happened during the four riffles? Mere eye contact and talking isn't going to be enough.
I point something with my right middle as i do the move
My 9 year old son's favorite cover for a coin vanish - "what's that over there!" Good misdirection needs to come within the structure of the routine. It really isn't misdirection away from something that is happening but simply direction to something that is happening. The more natural the better.