Here are some thoughts;
1 - Weapon skills replacing BAB altogether. How many combat skill there are is a matter of taste. 2nd edition shadowrun only had one firearm and one heavy weapon skills but 3rd edition had shotgun, rifles, pistols, smg, assault rifle, heavy weapons, launchweapon etc.
Either way, a good default rule is order because there is no way a PC will have all combat skills.
2 - Damage : There are no reasons the combat meter couldn't be maintained. You'd still get a damage code and a DC except they'd have to be adapted with the knowledge that a single D20 roll will replace several D6. Maybe the Damage meter could be maintained integrally or would have to be adapted a little, we'll see.
N.B. : It is understood that a Troll samurai who maxed his body (constitution) and has a level 4 dermal Sheath will have a higer damage save than the average joe (who used to have Bod 3 and now would have a damage save of +0)
When fired upon by a light caliber, it is common for our Troll to suffer no damage at all whilst average Joe still gets badly hurt. But against a very high caliber weapon such as a sniper rifle, our troll despite his 18D6 would frequently get very few success and resist the wound only a notch or two above the average joe.
How to reflect that? I am thinking that the rate at which you reduce the damage doesn't have to be linear. After all, the odds of getting 2 or 4 successes when rolling 6 dice were not linear either!
So for example, you could reduce the damage one notch by making the DC, two notch by beating it by 2, three notch by beating it by 5, four notches by beating it by 10...
Similarly, augmenting the damage would work along similar line.
Example: Neon Samurai shoots Wedge with an Ares Predator. The base damge is M (assuming we keep the same damage meter) . Neon Samurai hits with a success margin of 8. That would increase the damage to D. Wedge rolls his damage save and beats the DC by 10 (he's in his CyberZombie phase

). We're back to L.
Of course, that 2,5 10 scale is just something I pulled out of my hat and I'm not even talking about what the DC for the Predator should be, but I hope you get the gist of the idea.
3 - Skills will have a non linear cost that increase as the skill increases, just like in SR. I'm not sure the attributes should help determine when the cost of a skill increase upward as it does in SR 3e. In SR, your quickness doesn't increase your accuracy but it does determine how easily you can learn quickness related skills. In D20 your dexterity directly contributes to your accuracy. If it also helped learning the skills faster, the attributes would be too important.
Anyway, as long as the skill have an increasing cost, it will keep the game from spiralling upward into ludicrous bonuses.
Okay, it's late now and I'm tired. More later if I've got the time.