If the probability of getting 9-13 is much higher then, say, a 2 or 18 then the chances of your character making that DC 20 check are considerably more dependant on his abilities.
Yes, but I don't see what this has to with levelling. Since 'average' DCs are fixed at skill rank +10, luck is exactly as much a factor at level 40 as at level 4.
You just admitted that it is overpowered but (in your opinion) more realistic. You are basically saying that you feel everyone should just be doing more damage, for the heck of it...
Not so- as mentioned, dodge/parry/block would/could by used to compensate.
I don't know what RPG you are trying to play, but its far-and-away not 3.5 D&D. It's a bit closer to 2ed AD&D (you should go play that).
Yeah, been there.
Great, lets totally overly complicate the system and make combat reliant on a series of tables and 4+ rolls to figure out a simple attack.
I don't see what's especially complicated about opposed skill checks, but bear in mind that extra rolls would only crop up on occasions when you hit (which would be correspondingly rarer, due to dodge/parry,) or when confirming crits (and each confirmation is successively less likely to happen.)

I suppose you could call my suggestions inconsistent, but that's only because I'm not close to done yet. I certainly think that Hit Points, on balance, are an excresence that should be excised with all haste, but at least this kind of system puts melee characters on a par with primary casters when it comes to sheer damage capacity. Didn't think of that, huh?

What I find laughable personally is that- while his may have escaped you- when it comes to fixing balance and realism in D&D, adding 2d10 mechanics is waaaay down the list.