Disorganized post hitting on various subjects:
The entire philosphy behind DGS is different from the standard SOLDIER philosphy. DG was used to conduct morally objectionable experiments, some of which were pretty horrific. On top of that, when the Restrictors took over, the entire organization basically became a large scale exercise in survival of the fittest, where DGS were pitted against one another, to the death, in large scale mission and battlefield simulations.
The DGS were from all walks of life. Some were SOLDIERs, yes, but others were civilians, and I'm sure there were many members of the Shinra Army, polticial prisoners, criminals, and so on.
As stated in the intro, DGS included people who were kidnapped, people who had been injured and were taken there, people who were born there or could remember nothing before it, people who suddenly found themselves there, people who understand what the place was, and people who don't know anything at all about it.
Weiss and Nero wore SOLDIER-style uniforms, as did other DGS. They were born in Deep Ground, however, and they couldn't have been regular SOLDIERs. I'm not sure if I'd go as far as saying it was a disguise, it was just what their uniform looked like.
DG has a unique rank system that differs from the standard SOLDIER classification:
DG Drone: 3rd, 2nd, 1st
DG Scout: 3rd, 2nd, 1st
DG Trooper: 3rd, 2nd, 1st
DG Commander: 3rd, 2nd, 1st
DG General: 3rd, 2nd, 1st
Tsviet
Tsviet (w/ Color Epithet)
Probably all members up through Trooper were roughly on par with the various ranks in the Shinra Army. Commanders and Generals are probably approaching SOLDIER:3rd or 2nd levels, and Tsviet are at least 1st Class SOLDIER material.
By the time Tsviet overthrows the Restrictors and DGS starts heading out into the world, you're probably left with the stronger survivors, since the weaker members would've been killed off.
As for Cloud, yes, he's got natural talent, and his so-called "bursts of adreneline" are probably similar to the concept of a Limit Break, which you even see a little kid doing in FFVII. However, it's still pretty implied that a lot of his skill comes from Zack; we know that Zack at least showed him a thing or two, and when the Jenova cells augmented his memory and persona with what he'd observed from Zack, it stands to reason that he artificially "learned" a lot of Zack's skill.