It is possible. We see Spriggans summoning bears in Oblivion. I imagine some "druidic" Bosmer could also do it in theory[no source on that, just my supposition]. If Spriggans can do it, then it should be possible for others. Particular those who follow the ways of Kynareth/Y'frre.
You're thinking of the Spider Daedra of Mephala. They are considered very difficult daedra for conjurers to permanently bind in a "loyal state."
[1] Yes.
[2] The elemental Atronachs are akin to mercenaries. They will serve any Principality that "pays" them well. That is why they are common amongst conjurers(especially those we see in Skyrim). They can be "plucked" from many realms since they aren't tied down to any particular spot at a given time. Where-as summoning Xivilai may require some knowledge or awareness of the Deadlands, and Seekers may require some connection to Apocrypha. But Atronachs can be interacted with from many realms at once.
[3] I imagine they are summoned from the "ash of Red Mountain." Red Mountain is a "mythical" place in of itself so... yeah... Or perhaps, you are summoning their "spirit" from an outer realm, where monsters that do not align to any AE go to? Not sure on this. Easier to just say they are created by the mind(knowledge and understanding of Heart-Stones as taught by Neloth) or from Red Mountain. Take your pick.
The wolf spirits and undead likely come from the "outer-realms." I am reluctant to say Soul Cairn specifically. The Soul Cairn has it's own variant of Undead that we can summon. But I like to imagine the powerful undead from TES Oblivion(Lich and Wraiths) could also be from the Soul Cairn. Shambles also seem to be specific to the Shivering Isles, but I also find them very reminiscent of http://uesp.net/wiki/Morrowind:Undead#Bonelord. Perhaps being of similar design rituals. Them being found in Shivering Isles and not in Cyrodiil is more of a game-play issue to me.(complications of having SI creatures mixing with vanilla leveled lists)
The bound weapons in Skyrim may be ethereal, but if you inspect closely, you will see that they are still in fact, the same exact design as Daedric weapons. Just like the bound weapons in Oblivion being the same as Daedric.