Where does the yunkish slave army outside Meereen come from? I tought Dany freed all the slaves in the Yunkai and confiscated a good chunk of the Wise Masters wealth? Did she just take them by their word and didn’t check up on the slavers upholding their end of the bargain?

So this is a question I thought I had answered, but may have gotten eaten by a browser refresh or OS crash, because I can’t find it anywhere in my archives.

So where did the Yunkish army – which keep in mind, is only one part of a larger coalition which includes the forces of New Ghis, Qarth, Elyria, Tolos, and eventually Volantis – come from?

Well, a lot of them are mercenaries who the Wise Masters hired – the Company of the Cat, the Long Lances, the Second Sons, and originally the Windblown – because while Dany redistributed a part of their wealth, her terms that the slaves should be given “as much food, clothing, coin, and goods as he or she can carry” would leave the bulk untouched.

But I imagine your main question is about these soldiers:

“There were more, near as mad or worse: Lord Wobblecheeks, the Drunken Conqueror, the Beastmaster, Pudding Face, the Rabbit, the Charioteer, the Perfumed Hero. Some had twenty soldiers, some two hundred or two thousand, all slaves they had trained and equipped themselves.”

I think there are two explanations for where these slave-soldiers came from. The first is that the Yunkish simply bought them on the open market when they re-established slavery and began re-arming for war against Cleon. Certainly this explains sub-groups like the Clanker Lords.

However, this explanation doesn’t work for Yunkish commanders like the Little Pigeon and the Girl General, both of whom are described as having bred their soldiers, which requires multiple generations’ worth of time, and thus can’t have happened in the few months between Dany’s liberation of Yunkai and the second siege of Meereen.

My explanation for this latter group is that they were probably not in Yunkai when it was attacked. See, it’s rather unusual for Wise Masters to produce and train soldiers, since Astapor specializes in the Unsullied and Yunkai specializes in sex slaves. Given that they lead their soldiers in person rather than selling them to others, and that they’re ambitious for overall military command, my guess is that the Little Pigeon and the Girl General and their ilk were working as mercenaries elsewhere in Essos when Yunkai was attacked, and then came back home to take revenge on Dany.

How well organised are mercenaries in Westeros? They’re apparently not as prevalent as in Essos, and there’s the occasional mention of “freeriders”, but are there any larger companies of specialised troops, such as crossbowmen or pikemen?

Freeriders aren’t mercenaries.

Because the ruling class of Westeros relies more heavily on control of military manpower than the ruling class of Essos, it’s usually the case that mercenaries in Westeros are usually Essosi free companies who’ve been brought over as additional troops and/or specialized troops (Myrish crossbowmen, for example), whereas native Westerosi largely serve in the armies of their liege lords.

However, there is a history of Westerosi mercenary companies being founded as a way to get inconvenient fighting men out of the country following a major political rupture:

The Company of the Rose, for example, was founded by Northerners who refused to accept Torrhen Stark’s submission to Aegon the Conqueror, and preferred exile in Essos instead. Their departure for Essos meant that Torrhen wouldn’t have to deal with a large militant faction of nationalists, who might have supported his sons’ faction in Northern politics.
The Stormbreakers were founded in the wake of the Dance of the Dragons, and likely absorbed a lot of the excess soldiers who had been mobilized during the Dance and now had no peacetime employment. Based on the name, I wouldn’t be surprised if the original founders were Riverlander veterans of the Battle of the Kingsroad, but I would also guess that no small amount of their number were made up of the surplus Northmen who were left behind after the “Hour of the Wolf.”
The Second Sons predate the Conquest, which shows how long this tradition has been going on, and were formed more for economic reasons than political ones. As WOIAF tells us, the company was “founded by twoscore younger sons of noble houses who found themselves dispossessed and without prospects.”

It is important to note, though, that all of these free companies left Westeros and worked exclusively in Essos – which was probably quid-pro-quo for allowing them to be formed in the first place.

How many men do the brave companions actually have? And how does such a seemingly large multinational company come together, and where did Tywin find these evil fuckers?

They’re not that big, around 300 men. They’re a pretty recently-founded company, although they predated Vargo Hoat.

As for where Tywin found them…although it’s not stated particularly clearly, Tywin clearly put the word out for mercenaries when he called the banners at Casterly Rock.

Tywin didn’t seem to get very good/many mercenaries, for various reasons. My theory is that Tywin has a bad reputation among mercenaries for using them as arrow fodder to keep the wages bill down.

Among those he did get, the Bloody Mummers are in Tywin’s army after the Green Fork but we don’t hear of them before that although logically that means they would have had to be at the Mummer’s Ford and Tywin’s rampage across the hills of the southern Riverlands.