1.Mostly, no, you don't need to. Some of the weapons have nifty features, though. Even for all I might make them sound cool here, though, you can easily get all you need out of them with only a couple weapon forges total in the main game.
-Marisa's brooms can get you 6 mp regen per turn, and mp drain on physical. Infinite magic! The matk boost isn't too high per broom upgrade, so you don't need to make new ones often.
-Sanae has MP drain on physical, and decent attack power on her snakes, helping her spam buffs in randoms or just plain attack. Some of them have nice poison, too...
-Nitori's gun slayers (or Elemental Bullet) come in handy sometimes, plus Rage Eight is pretty strong. The third gun, that also carries Transcendent Slayer, is a pretty good make, it comes up for a few bosses with that slayer type... and murders mindflayers.
-Sakuya's weapons are all powerful and have cool slayers, but you don't want to make them all- you'll run low on her specific material. Definitely want to make the Vyse Sword, though.
-Alice's Rainbow Greaves give a wonderful resist set.
-Byakuren's Deva Scroll is one of the very few weapons in the game that boosts IND. Definitely worth making. (For that matter, beneficial buffs get increases in power every 10 IND up to 100)
-Some of Mokou's fists inflict status effects. Since the fist tree has a bonus that doubles the chance to inflict them, they have a very good hit rate, even if Mokou's IND is terrible. It's good to disable some pesky enemies...!
Alice... her Marionette Parrar skill is her staple skill to spam forever, even in randoms; it's drastically powered up by one of her Growth trees, and once you get 25 points in said tree, it's simply incredible. Even if stronger when in the same column, it's still very powerful if Alice is separate. She also has skills specifically for defending against certain elements, which are useful when you have to face a lot of scary attacks from said elements; and London Doll is cool.
Alice is more of a boss character at first, but if you're having troubles living in random battles, switching her in to tank your party usually makes a world of difference.