Archives aren't related to Artifacts. They can be crafted into Permits required for normal upgrade-related equipment past level 60, which is the big bottleneck for leveling characters past that point. It takes 14 Weapon, Armour and Accessory Crafting Permits each to upgrade a single character's equipment from level 56 to 77 to open up the final promotion at level 80. The only ways you can get those permits are from the Daily Missions past level 30 (one per day), crafting Archives into them (20 Archives > 1 Permit, also costs 300k Silver Coins), or from login rewards/event rewards. If you're diligent about gathering the Permits/Archives, you should be able to upgrade one character a month to the final promotion, with some left over.
So that's different than Fusing. Fusing is the simple act of turning two artifacts of a certain level into a higher level one. And you can Fuse more than your one star stuff! There's a dropdown menu at the top-left (it should say Class 1 to start) that lets you pick what level of Artifacts to Fuse. You can use that to try to Fuse your higher level things, too. It's just tricky at the start because, as you said, you can make use of even your junky items.
I did well with my Fuses! I got a +35% Earth Damage accessory (hello, Zhuge Liang), a +20% Offensive Tactics accessory (Cai Yan will like this), and a Heroic Axe that gives First Strike (if the equipped character is attacked by an enemy in range, he'll actually turn the tables and initiate the attack himself, this is great for Lu Bu and Meng Da who have ways to stop enemy counterattacks). So now I have some direction on which character to level up next. Lu Bu! I choose you! Then Zhuge Liang with whatever permits are left over.
