Trigger Warning

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.

They've already made a token effort by besieging Storm's End but they are big and strong enough to do whatever they want, what's Aerys gonna do? Declare war on them? He's a paper tiger at this point.

It's feudalism, lords send token forces all the time or keep men back for the harvest or out of disdain for the cause. Logistics and the urgency of the campaign might affect how many men can be raised, bad harvests, plagues, weather, the finances of a lord or town. Military numbers fluctuate constantly due to many different factors especially without rigid systems of conscription. Regarding the Royal army, they could have mercenaries, loyal men from different regions that wish to serve the crown or seek the favour of the king, they could have pushed men into service from King's Landing, the city is huge. There's plenty of options.

This was my take as well and in my opinion an altogether more interesting and human moment than an actual grand secret.

I'd imagine all that matters is the idea that someone's a guest and should expect safety in any place regardless of the location. If I invited you into a random cave offering hospitality then clubbed you over the head while you ate I'd think I'd still be violating guest right in principle because it's about that specific situation, not whose cave it is.

Not even gonna raise an eyebrow until it's printed and shipped.

Defeat in detail is explicitly using overwhelming force to engage the smaller sections of an enemy army. While I'll concede that defeating Jaime's force before engaging his main force is an example of this it's a poor one. Jaime's force is superior to Robb's and Robb's strategy relies entirely on Jaime's lack of a strong screen of scouts and Jaime splitting his forces. While this works out fine and you can argue that it worked because they knew Jaime would behave this way it's hard to justify as a good use of defeat in detail when it relies massively on huge enemy mistakes and holds huge risks. Defeat in detail is entirely about minimising risks, had a single man seen Robb's men and reached Jaime then Robb would be entirely outnumbered. I really can't see taking such huge risks and potential to be outnumbered as a good example defeat in detail.

I think it's a stretch to describe as an effective use of defeat in detail, sure he defeated the weaker arm of an enemy army but his main force was sent to engage the enemy's main force and was defeated. He even defeated Jaime (EDIT: Jaime's army as whole, not Jaime's little anti raider force) with an inferior force so it's not even like he concentrated his power on the weaker Lannister army. If anything he lucked out that not a single Lannister scout managed to report his movements.

Why would you legitimatise the people you just usurped by giving them a powerbase and the traditional seat of the crown prince. Offering mercy to rebelling vassals and offering mercy to the family you just took the throne from are completely different.

I really think this is an oversight on GRRMs part, either that or they were already in country and there's opportunity for soldiering in Westeros we just don't hear about because it's not important. Tywin really had no reason to be bringing sellswords over from Essos at that point and I doubt he'd be bringing small sellsword companies to Lannisport were he secretly preparing for war anyway, why do something so obviously suspicious for so little gain.

Shipbreaker Bay is famous for its calm waters and pleasant weather.

He might be capable of being a mean bastard but that doesn't mean he can summon storms unless...

Sure but I doubt they'd get that far without her being his mistress first.

Does passing the Golden Tooth really count when it basically comes down to... lol magic wolf

Renly was scheming to make her Robert's mistress, most likely with Tyrell approval.