In AGOT it is mentioned that part of the crown’s debt is to several Tyroshi trading cartels. What are those and how old is the word cartel itself anyway?

A cartel is a group of economic actors – either sellers or buyers – who agree to cooperate in an attempt to create an oligopoly that can fix supply and/or demand (and thus prices), market share, and so forth. A trading cabal would probably be focused on trying to control a geographic market, or on trying to corner a given commodity.

In terms of its origin, the use of “cartel” with regards to business dates back to the late 19th century, where it was used in Germany to describe business organization in the new industries (whereas in the Anglo-American sphere, the terms “trust” or “combination” predominated).

The Myraham is called a trading cog from Oldtown. 1) Does that mean that its captain pays taxes or fees to Oldtown? 2) Does he own the ship? Or do the Hightowers own it and the captain just uses it in return for taxes? 3) Does this apply to all trading vessels in the Seven Kingdoms? 4) Could King’s Landing have had a merchant fleet, or it never needed it?

It means that whoever owns the ship, and it could be the captain or it could be a merchant or a consortium of merchants or a nobleman (although that’s less likely), is based out of Oldtown.

In terms of taxes and fees, you’re dealing with two things. The first is that the owner/s pays taxes to House Hightower by virtue of being a resident of Oldtown, but that’s no different from any baker or blacksmith who also is a resident of Oldtown. The second is that when the ship is in Oldtown, it pays tariffs and excise taxes, harbor fees and warehousing fees, the same as any other ship in the port (although it’s quite likely that the Hightowers charge a lower rate to resident merchants as a way of stimulating local commerce).

Looking at the sources, it doesn’t seem like the Hightowers have a proprietary trading fleet in the same way that the Redwynes do – rather, the Hightowers’ navy is meant to “to protect his trade.” Nor does King’s Landing have a proprietary trading fleet; they have a lot of ships based out of that port, but the crown doesn’t own them directly, although Littlefinger probably bought quite a few of them using embezzled royal funds.

Is the three hides of land offered to each of Gregor’s men by Ser Bonifer a fair reward for their military service?

Three hides of land is a good bit – it’s a bit below a “knight’s fee” which was usually five or more hides, but a single hide enought to support one family, or 30 modern acres. So each of Gregor’s men gets 90 acres of land, which would put them solidly in the ranks of the yeoman – below the knight but above the knave, as it were.