Trigger Warning

I'd imagine they attacked as soon as they got enough men through the gate to overwhelm the defenders in that area. They'd have to micromanage thousands of men that know they're giving up on potential plunder all the way up to getting men into the Red Keep, then into Maegor's and around the king just adding layers and layers of complexity to the plan and this is assuming that Aerys wouldn't question why Tywin needs men in the Red Keep in the first place. The citadel is already garrisoned and a potential siege could mean days or weeks of fighting over the city walls so why would Tywin's men need to head there right away? Beyond that even if they got to the king that still doesn't mean fighting won't break out in the city (when there are literally thousands of royalists defending it) in which case the men would likely still plunder it. The reality is that when enemy cities are taken by storm they are plundered and even though they used subterfuge to overcome the outer wall they still stormed the city the same as they would a breach, Tywin's not going to come up with some convoluted plan to stop this when it's just the norm of the society they live in.

This is assuming that Walder and Roose have no say at the negotiation table.

The scale of the castle's so out of whack that this is basically impossible to even speculate on. GRRM describes these huge structures but then has people interact with them as if they were much smaller so it's basically not worth the effort even thinking about too much.

It doesn't matter that he was doing his duty in serving Aerys, I'd imagine that he was simply pardoned for being an enemy of Robert and fighting against him. I wouldn't focus too much on the technicalities of it it in some sort of legal context.

I don't think anyone would be questioning the rape if it wasn't for the fact that he's a bit of a dick and Arya killed him which puts some people on the defensive, it's pretty obviously written in a way to suggest he was innocent albeit naive about the consequences of sleeping with a lord's daughter.

The guy commanded the city watch of the largest city on the continent why would he not be a contender.

I think they can wear whatever they want so long as it's black.

That goes without saying but YOLOing it on one battle is not a particularly sound basis for a campaign when your forces are more or less even.

Renly cannot win, his enemy has a magical assassin he doesn't know about.

It's a nice place to starve or freeze to death, don't know why they'd need to bother attacking it.

Doran's a victim of the plot needing things to happen but since that's not an in world explanation he's just a plain old idiot. I certainly wouldn't send my son halfway across the world into a region embroiled in war with a few men just to show a queen an old pact and offer her a marriage alliance, send some fucking goons Doran come on. If she agrees she's gonna say yes for the promise of Dornish spears not bloody Quentyn, any trustworthy retainer can deliver that message.

Pitched battles of similar numbers can go either way very easily, in fact they can easily go either way even when the numbers aren't evenly matched even with limited tactical control from the commanders. It's why military leaders spend most of their time avoiding them, so the answer is basically just yes, he could have but analysing how would be so speculative as to be almost pointless.

He also goes on a petty rant about it to Ned's grieving widow.

I can't believe Stannis didn't think of raising another lord's men under the guise of a training exercise.

I don't think it'd be that interesting, Mace would just join the rebels and Aerys' fall would come all the sooner. Mace is one of the most powerful lords in the realm, Aerys saying whoever kills him gets his lands doesn't mean much the same way it wouldn't mean much if he declared the same for each of the rebellious great lords.