Do upgrades from one guild apply to all of that class type?

As far as I know, heroes don't start with upgrades. Heroes can buy upgrades by paying small symbolic values in the guild (warriors have to pay 5 gold for their first upgrade). Think of guilds as if they where personal markets for the heroes, but not necessarily only for the type of heroes in there; warriors can buy a poison upgrade in rogues' guilds. Shelter/healing can only be reached at their home guild still. You can see those heroes abilities (basic and upgraded), stats, bag items, info and more, by clicking on the top-left info icon of it's portrait.

Something else you should know is that heroes have to pay taxes. When they kill a monster, steal from a tomb or open a chest, they have to pay taxes to the kingdom. Those taxes are left in the guild, added to the gold from sold items, which will be later collected by the tax collector. If you hover your mouse on the gold coin icon, on the hero's bottom panel, it will tell you how much money from the total this hero has to pay in concept of taxes.

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