I noticed that mages skilled in Swordsmanship become Guardians. Do they use Anti-Magic or simply have resistance? Do all mages gifted with the sword become Guardians?
Resistance kind of. Magic used on them or in very close proximity to them is sucked through their reversed bridge. Remember me saying magic is drawn across a bridge connecting worlds? Well guardians passively send that magic back. No, not all mage's good with a weapon become guardians although there is tremendous pressure to do so.
While mage's are feared and hated, Guardians are generally looked upon favorably and sought after for their magic resistance. Guardians are favored as personnel bodyguard for many noble houses throughout the kingdoms, for both their skill with a weapon and their aforementioned magic immunities (they are still vulnerable to certain forms of magic. For example, if a geomancer flings a boulder at them they aren't immune to heavy things flying at deadly speeds)
At one time, at to some extent today, there was animosity between mage's and guardians with mage's viewing the latter as 'sell outs'. Though many mage's with that mindset went on to leave the tower as Malfears acolaytes. Although Guardians have a role in the protection of Tower mage's they also function to suppress other mages who practice magic outside of the tower. For that reason relations between mage's and guardians vary wildly.
Back on topic, as a rule of thumb you shouldn't expect your character to be proficient with weaponry unless they have some points allocated to it. For example strength would allow you to overpower enemies, precision would allow you to out finesse enemies, and you could spend unique traits to also improve your characters weapon competence. In other words a pure Mage whi engages a soldier in physical combat will likely die, unless the soldier is stunned or otherwise helpless.