Yes, trash mobs can drop different color items, the colors represent the rarity etc. There are also hidden chests throughout the entire world that you use lock pics to open. If I remember there are 4 different level chests, the higher the level, the less time you have to pick the lock. These can also contain rare, high level items and also gold. These treasure chest disappear once opened and they are on a timer and will reset after a while.
If you find a rare item, you can get it modified, but mostly items that are leveled up by a crafter are home made items. But the big thing here is that the material needed to level up an item is pretty rare. As you find items you can sell them, upgrade them or deconstruct them for their materials. Every once in while, you get lucky and when you deconstruct you get a rare items that allows you to level up crafted items. But this does not always happen. It is common to find items that take a item from Level 1 to Level 2, but the items that take an item to Legendary Status are far and few.
Then there is the risk/reward that plays into leveling up an item. Early on, if you want to take a White item and Level it up, you need a specific item to do so, but if you want to be sure it takes effect, you need multiple of the rare item that allows it to level up. For example, the game will say "If you only use one rare level up stone to level up this item, you have a 30% chance to succeed, but if it fails, you lose the rare stone and the item you are trying to upgrade". If you use 2 of the rare items, it could jump to a 60% chance of success. So there is a gamble in upgrading items, but also a cost. A crafter will not do this stuff for free due to having to find the special items to level them up etc. You can apply enough of the special upgrade items to make sure it is a100% success, but you are also using a lot more rare items to accomplish it.