If you ever get the chance to talk with a "real" climber, one of the people that does it ALL the time, check out the calluses on their fingers. One of the guys that I learned to climb with(who has since moved Yellowstone for climbing) developed calluses so thick that they allowed him to do full pullups on a row of dimes glued to the top of the doorframe. To someone who is a very good climber, you'd be surprised what sort of holds can be found.
Also, the musculature of a climber is similar to a martial artist, in that they use a full range of motion and have power throughout that motion.
I climb recreationally, and have maxed out (so far) at 5.11, which is pretty good, but nowhere near the top of the sport. The best climbers are doing 5.14s routinely now.
The particular pic you posted looks to be from American Forks Canyon, nice place, only been there once. Judging from what I can see of that route, it looks to be a 5.10 or so.
Now that I've babbled about climbing in general, here's a little bit about free hand.
Essentially, free hand is generally used as a way of making an "easy" route more difficult or as exercise.
Most climbers will not do free hand, as it's antithesis to what they've learned. (The rope is your friend, never forget your friend)
For free hand, you'd generally pick something of a lower grade than your maximum climbing level. For example, since I climb 5.10 routinely, I'd probably say 5.8-5.9 would be where I might be comfortable free climbing as the degree of difficulty would be reduced, resulting in less liklihood of falling.
And in reference to hand strength, well, let's just say you don't want to get into a handshaking contest with a climber. I've left indentations in a door frame when doing grip pullups (fingers sandwiching the frame, nothing really wrapping around a top) and have never needed a tool to crack even walnuts(generally opened with a small hammer here in the US).
Well, I hope this answers some questions.
TC