1. To make a monster's item spawn with random affixes, all you need to do is assign them a magic (or higher) grade item with no preassigned affixes. However, I would recommend against doing this. Some of the affixes can cause a pretty unbalancing change in the monster's damage output, with absolutely no visual cue for the player that this monster is more dangerous than the others who look just like him. Some of the affixes are also pretty annoying from the player's perspective.
2. To make a monster's item spawn with fixed affixes, simply assign them an item with fixed affixes.
3. There are two ways to make a monster spawn with a randomized item:
a. Make a spawnclass of the potential items and assign the spawnclass in the monster's equipment tab.
b. Make multiple clones of the monster, assign each one a single item in its equipment tab, create a spawnclass of the multiple clones, and edit the existing spawnclasses to replace references to the monster unit with references to the spawnclass.
The advantages of option b will become clearer in a minute.
4. To make the monster drop the item it's holding:
a. I know of no way to make a monster directly drop an item that it has equipped. Maybe the drop_on_death flag does that. You can experiment and see if it does. (However, that would be problematic from a loot balance standpoint because it would be a 100% chance to drop. You could mitigate it by using clones to simulate a lower drop chance.) As per Dee's post below, putting the drop_on_death flag on the item will make the monster drop their equipped item. This may be problematic from a loot balance perspective, since it means the monster will be dropping this item 100% of the time. A solution would be to clone the item, giving drop on death to only one clone, clone the monster (as per 3b above), and give that clone with the drop_on_death item a much lower chance to spawn.
b. If you used the clone method (3b) above, then you can simulate a monster dropping them item it has equipped by assigning the same item it has equipped to its treasure classes. (This also solves the loot balance problem since you can adjust drop chance directly.)
c. To expand on 4b, since you probably don't really want to put affixes on the item the monster has equipped, you can do this: Set the equipment for each clone of the monster to a no-affixes or fixed-affixes item modeled after the vanilla monster weapons. Set a treasure class on each clone to a spawnclass made of randomizable items with the same model and skin as the item the monster has equipped.