1. For bullseye and target shooting, 1 or 2 eyes doesn't really matter. Really bearing down for accuracy, one is better. For defensive shooting, requiring periferal vision, and moving targets... 2 eyes it the best. Try squinting your non-dominant eye at first, forcing your brain to focus the dominant eye, but keeping the second eye open.
2. It is true that the bullet is long gone before the recoil is felt, but it is the fine manipulation of the gun with the trigger finger that can throw off the point of aim before the shot. A firm grip, and constsnt trigger pressure, and LOTS,. and LOTS and LOTS of practice will help. Try keeping just the tip pad of your finger on the trigger (unless you are pulling a long double action gun). Pulling or pushing with the trigger finger can move the front blade 1/64th of an inch, that can result in a lot of deviation at yardage... ALSO, how far away are you shooting??? Start in close at 5-7 yards, and when you can shoot ragged holes at 7 yards, move out slowly to 10, and 15 yards... Beginners should NEVER shoot at 15-25 yards... You'll just get frustrated.
3. Most factory ammo for a 9mm will be 115-124 grains... Not a problem for your gun. Stick to inexpensive full metal jacket ammo for practice. At the yardages you'll be shooting, the point of impact will not vary much between 115 and 124, or even 147gr ammo.
In the big picture... everything is relative, and relative to distance. At 7 yards, a "good" group for most pistol shooters is 4-5 inches. After months, and years of shooting, 2-3" is better. With a very short barrelled, short sight radius gun like your Taurus, anything on a paper plate at 10yards is good. That's no target gun with a match barrel, target trigger, and precise sights... It's made for 5-7yard shooting into a defensive size target. If you want tiny groups, shoot a more precise weapon.