You will always have a spell in use on Oblivion. If you don't want to use that spell, then simply select a different one. :)
Cast spells
Cast a lot of alteration spells.
The dark elf is very good for spells.
You cannot construct your own spells as you could in oblivion, you must find or purchase spell tomes and consume them.
30 second invisibility
They are in all of the cities mages guild mostly or in the ARCANE UNIVERSITY.
It should be in the list of all your other spells. Cast it normally.
To kill any kind of ghost or spirit in TES 4: Oblivion, you need to either use spells, or enchanted, silver or daedric weapons.
There isn't one. There is only weakness to fire, frost, shock, magic, and normal weapons spells in oblivion. There is a weakness to disease spell in Morrowind, i think.
My best bet is that you have not saved the game. That's the best I can think of..
There is no option to make custom spells like Morrowind or Oblivion. You have to stick with the ones taught to you by the spellbooks you buy.
Go to your Backpack and go to Character and click on pets. Then hit 'Unequip'.