Khakiasp already answered all the other stuff, but to clarify this question, it all varies depending on the enemy. Most don’t, but some of them can randomly drop what they’re using whether that be armor or weapons.
However, not all of it’s random. In the cases of some enemies, (usually non respawning or less frequent ones), there is no random drop chance, and instead killing a specific enemy will get you X scripted drop.
If you need weapons, check with merchants, the ones you find in the early game sell at least one weapon in most of the major categories so you can try out the different movesets. You might think buying is a waste of Runes if you can find the weapons later, but in reality you usually can’t- Eg. I’ve never found the basic Short Spear out in the world, I had to buy that from a merchant