I'm the odd guy out. I shoot very differently than most guys - the theory is different when your heartbeat jumps the sight window off the grid. I use an old military take-up trigger and I anticipate my shots intentionally, waiting for after the lub-dub, re-aquire the point of aim and pull the trigger.
I use a harness cinched up very tight, control my rifle with both hands, vary the hold with different style stocks (greatly prefer a Nathan Rapose-style thumbhole stock), and prefer the slightly back angled grip with a significant belly in the middle of the grip.
Answers are for bench and prone and for three rifles 222 REM, 270AM-braked 338 RUM-braked
#1 Do you control the rifle with both left and right hands?
Only one hand with the trigger finger touches the rifle. Other hand is on the beanie bag.
#2 Do you vary the hold according to the caliber and weight of the rifle?
No. A slight/delicate straight pull back with the trigger hand.
#3 Do you vary the hold depending on the field shooting position?
For long range hunting the position is always prone unless something miserable happens.
#4 Do you prefer vertical pistol grips vs curved grip design?
Vertical pistol grip much much more preferred!!!
I follow Roy's approach and preferences pretty closely for prone. Unfortunately, many of my favorite hunting areas either do not have the terrain for a prone shot, or I am not allowed the time to set up prone to get my animal and can end up in a variety of different shooting positions, using different kinds of rests. For prone most all my rifles, regardless of caliber are shot the same way, and I get consistent results. For varied positions at long range I have found the lighter recoiling calibers like my muzzle braked 6.5x284 are significantly less sensitive to varied shooting positions for long range work. I have also found that for these conditions, and my physical make up that the curved grip design gives me more flexibility, comfort, and control from different positions without trading off my accuracy when prone. While the trigger pull length is the same between the two styles, the straight grip requires a more extended arm due to the straight design. I don't state all this to be gospel, but it's what works for me.
"Let us speak courteously, deal fairly, and keep ourselves armed and ready"-T. Roosevelt
I always shot one handed in the prone position off a bench rest and let the rifle free recoil until I go my first light rifle (Tikka T3 Lite 30-06). The Tikka needs to be held tight (into should and down on the forearm).
When I shot match we used a shooting sling, to me that is probably going to be the best set up for accuracy unless you have a 12lb+ rifle that is set up to free recoil or you are shooting a light round that doesn't recoil much.
On another note, I try not to bench shoot much other then sighting in or trying new rounds. I have taken many deer off-hand standing out to 300 yards with no problem. Farther out I usually drop my back pack or find a rest. The point is that if you hunt, shoot like you hunt. I would rather look at a 3" group I shot from the standing position at 100 yards then a .7" group from the bench. I spent a lot of time shooting a 8" gong at 300 yards while standing with my rifle (rifle was zero'd for 300). I would shoot like shooting trap, bring the rifle up and fire quickly. That and lots of gopher shooting with my scoped 10/22 made me a pretty fair marksman.
Greyfox - I'd agree that lite recoil guns are more forgiving to variations.
Major S - We should all learn to practice the more difficult positions like you do. Out in my neck of the woods, we generally set up on a high point and rely on the 7 x 50 binoculars to hunt for us, so prone and seated are the positions that get the meat in the freezer. Long, cross-canyon shots make range estimation difficult, so nobody faults each other for using rangefinders. Flat-shooting mag's are the norm. I sneak by (if there's not too much wind) with a .30-'06 or an Ackley-Improved 7mm RUM, the latter approaching appropriate for long canyon shots. I pass on brush-busting shots, preferring to wait out an advantageous situation. I do love getting the damn harness off after my shot.
shooting prone I use my shooting hand. only place my finger tips on the grip and lay my thumb gently on the gun. depending on target or hunting ill either use a bean bag or my hand to support the butt of the rifle. It also helps aiming. what this dose is eliminate the pulse and breathing factor when taking shot. I shoot with a bipod and I barley load it. this will help keep your target in your optic. with larger caliber rifle I use muzzle breaks so the recoil is as bad and you don't have to worry about loosing sight of your target. typically long range is only done in the prone position. I prefer the curved style grips. hope this helps