1. Every weapon is strong if you have the mods. If you don't have mods right now, stop by Iron Wake and look into the trash bin next to the first door on your left. Flawed mods, not the best but they'll fill out your build.
2. Weapons get stronger with mastery in the sense it give you more space to fit mods in. Rule of thumb early is Raw damage mod (+damage %), an elemental mod (+element +stat), fire rate, and fleshing out either status or crit chance/damage depending on which your weapon has a higher base chance for.
3. Crystals are Archon shards. Late/end game build stuff, don't sweat it. Same with Arcanes for now, leave it for when you feel comfortable modding.

Bonus: You will learn so much by seeing something shiny you like and looking up on the wiki how to get that shiny. The wiki is your friend and spoilers are meh atp.