I've checked through the Chrome books, Solo of Fortune and a pile of other source books, but the only info I can find on Shotguns is in Friday Night Firefight from CP2020, so these are all the rules we've got to work with and they are obviously confusing and lacking.
In the games I've played and run shotguns weren't used very much as range is a little limited, they're great for CQB, but most solos ended up using massive pistols or other weapons.
For me, the critical point of the shotgun is that the grenade scatter pattern is used vertically, rather than horizontally - so that gives direction of scatter away from the target in an XY direction.
Ie a scatter direction of 8 and 10 is directly above the target and 3 and 1 is into the ground below/in front of (the floor) the target, 5 is to the left and so on.
So; with that in mind shotguns become a lot more sensible; so to the questions:
1. Do we roll on the Grenade Table to determine the true center?
Yes, if the shot misses determine the direction of the shot going wild using the grenade scatter table but as XY direction as if facing the target (as explained above) take some sense in this, so if you scatter 10 metres down then you're just pumping lead into the floor.
2. If the true center is in front of or behind the target, does that still count as a hit?
Scatter is XY, not Horizontal; but if the shot is in front, (ie roll of 3 and 1) then depending on the scatter roll and range they may still be in the effect.
Short is 1 metre pattern, deviation of 1 hits the original target
Medium is 2 metre pattern, deviation of 1 or 2 hits the original target
Long is 3 metre pattern, deviation of 1 to 3 hits the original target
3. If the true center is left of the target (5 on the grenade table) and I roll 10 on the second d10, did I fire my shotgun 10 meters left of the target? If not, how do we actually resolve a miss?
So 5 is still left and 10 is a massive scatter, so unless there's something important to the left, yes, you've pumped your round into the wall.
FYI, I have always played that unless there's something nearby a scatter of more than 5 is "pump your round uselessly into a cinematically damageable object."
4. Below the Shotgun Table, the rules say: "in six foot hallways, there would be no way for a target to escape taking wounds no matter how much his reflexes were boosted." But if that's the case, what's the purpose of rolling to hit? And how does REF help you escape taking shotgun wounds anyway?
This is half a fairly "fluff" statement and also more than likely an old rules typo that they missed; in very early versions of CP2020 (CP2013 I think or some other variant) you could "dodge" bullets with a reflexes+athetics roll instead of a straight target number, so I think this is something that wasn't tidied up, one of my CP GM's certainly played this rule and he was a stickler for rules.
5. Where does the target take the damage? Is it spread over all the limbs and the torso? Do we still roll for hit location?
RAW: There is no indication of where the damage is, it hits a single location as usual, so apply the damage to a single randomly determined location as usual.
Me: On a hit if the shell scatters in a particular direction I discount hit locations "away" from that location (Like "head" if the shot goes down) and reroll the damage, I did try breaking the damage down into d6 blocks, rolling for each one, but this got very tedious and also made shotguns very crappy against even basic armour, when they'd blow through kevlar in a close focused blast. So, single location for damage.
6. What's the purpose of the -2 penalty for consecutive shots of an autoshotgun if the shotgun either can't miss or the rules provide no way of resolving a miss?
Resolved above with the questions; you can pump out the shells, but who knows what the hell you'll hit as the gun leaps all over the place!