Buying a 'poor' weapon.

No, the stats of a weapon don't change when you level up or use them over time. Leveling does, however, influence weapons that drop as loot from monsters, as well as allow you to buy more powerful gear from other players through either trading or the market that would have previously been level locked.

The only item that could be considered to improve with use would be the harvesting tools, as they can be upgraded with crystals upon improving each specific skill and advancing to a new area.

Gotta get drops. I'd say roughly 8:1 ratios for each category. So, you'll find 8 poors for each basic, 8 basics for each standard, 8 standards for each refined, etc. I've never seen above refined drop, I suspect they're not in the game yet. 1 refined ~ every 500 items drops seems about right, but I haven't actually collected data.

Should note that you can also burn 50 crystals to make an item 15% better, but you can't do it multiple times and the buff only works for you, so you won't get any higher prices if you sell it later.