Rightclick -> Abilities -> Disable Ability on the right -> click No to unhide a hidden ability. If an ability has a weapon requirement they won't show up in battle unless that weapon is your currently active weapon, secondary weapons don't count until equipped. Mastering an ability defaults to hiding the base version of the ability to avoid clogging up the weapon menu.
The game doesn't stop you from equipping two of the same weapon, but same rules apply, secondary doesn't do anything until swapped. Going to the Progress- >Equip menu in camp lets you decide what your primary and secondary weapons are.
I'll look into the weapon name display and ability dictionary spacing things, see if I can replicate and fix if so!