Some rank A weapons can be evolved twice to SS weapons and you should definitely keep them. You can tell if they can be evolved twice as they will have two spades in their item description above the uncapped diamonds as well as having a cost higher than 10.

The upper right corner shows the best weapon to go with your character job. This means that using this type of weapon will give a variety of buffs to your character and is recommended.

You can obtain regular jobs from the story, S and SS jobs drop from the gacha. What differentiates them is how much their common skills boost stats by. Regular character jobs provide a +50 boost to stats for their Common (共通) Skills. S character jobs provide +75 to stats, SS jobs provide +100.

Leveling up your weapon job will boost your power for that weapon. 

Job skills however will only apply to that specific character and job. Just because it adds the same weapon stats doesn’t mean it will apply the boost to a different job.

Using other types of weapons will at most give you no bonus and might give you penalties.

You can see your character’s main weapon and usable weapons, as well as its main weapon’s bonuses in your character weapon page.

When you are using a general job, there is a 60% bonus in the corresponding character area, plus 10% for the breakthrough card lv2 and only 10% in non-regional maps.