Fortresses in Harry Potter Wizards Unite are the Pokemon Go equivalent of Gyms, with some notable differences. Fortresses have different Chambers within them that you need to unlock. Battling with friends is indeed possible in Fortresses, and cooldowns are far shorter than in Pokemon Go! In Fortresses you battle anything from Dark Wizards to a variety of Magical Creatures for rewards. The difficulty of each is determined by what you choose with the rewards for winning following that difficulty.
In battles with Dark Wizards, Magical Creatures, etc. both sides have Health that needs to be watched. Potions, of course, can be used in battles to heal when your Health gets low as well as to help make your spells more effective.
While the number of enemies you face does increase when additional wizards join you in battling at a Fortress, each profession has advantages and disadvantages against the different kind of enemies you face.
The difficulty of the enemies you face in a Fortress is determined by 1) the level you choose to battle in the Fortress and 2) the Runestone used. Higher levels for both mean more difficult enemies, and the Runestone determines the type of rewards you will receive from completing the Fortress battle.