If you already have 20 bonus characters and try to recruit a new one, you'll be prompted to delete one of the existing 20, so you don't actually need to kill them off. Of course, this is entirely optional; if you clear the SpotPass/DLC battle just for Exp, you can choose not to recruit the character and not have to delete one.
As for items in DLC, it's a bit inconsistent. The first two map sets, Spirit Talisman and King vs. King, take place on FE1's Ch1 and FE4's Prologue, respectively. As a result, they have two villages, which you can visit for random items each time you play the map, ranging from terrible (Wooden Stick) to awesome (Tomahawk, Fortify). Nothing you can't get outside of DLC, but plenty of things that are rather limited. The next two maps sets, Red vs. Blue and Light vs. Dark, take place on FE7's Final and FE9's Ch8, and so they don't have any villages with items.
Of course, this is all looking at just within the map. Several of these maps have their own unique prizes upon completion: The last map in each set gives you a scroll that teaches a skill you can only get through that DLC, for a total of four such skills, and the second King vs. King and Red vs. Blue maps have an item that allows characters to access a new class, adding two more classes, one for each character. (The classes are gender-specific, but every character can access one of the two.) For both types of items, you get one for each time you play through the map, so you can get as many copies as you want by playing through it repeatedly.
Now, those are the most standard sets. For the other maps, it gets a bit more irregular. In the Gold and Silver map, every enemy drops gold, which is the point of the map; you can get massive amounts of gold every time you play through it. Entombed Heaven throws a bunch of Entombed at you for Exp, but you don't get any items there. Infinite Divine Weapons is a much more difficult map with three chests, each one having a random, otherwise unique legendary weapon, although there are a couple of oddities tossed in as well. You also get a Silver Card for completing it, but you won't get more Silver Cards by replaying it if you still have the first one, since you don't have any use for multiple.
Then there's the Other-World Resort maps. In the first one, the boss drops a Master Seal as a bit of a random bonus, and oddly, the map has 18 event tiles instead of the usual 2, giving you a lot more chances for other random items, which you can get on any map. Can't say about the other two, as they're not out yet, but they should follow a similar pattern. The first two Ultimate Training maps have no items, other than the event tiles, which applies to all maps above as well. The third has two chests, which have their own random items, and seem to tend to be better than the ones in ST and KvK, which makes sense as a much higher-level map. The fourth isn't released yet, so who knows. And of course, with no Future of Despair maps out or even any information about the gameplay at all, we can't even guess about what those might have.