You should be able to remap your controls to put spell casting on any button you want, but yeah, there is only one spell casting button and it is independant of your equipped weapon, so you can have a weapon out and cast spells at the same time.
A mage can wear anything, but there is a spell efficiency penalty when wearing armor. This is most important with spells like command, fear and turn undead. The most powerful spell in the game is level 25 and at higher levels, you will encounter enemies that are higher than level 25. However, a level 25 spell will affect any enemy in the game. The result is that if your character is wearing no armor, their level 25 command, fear and turn undead spell will work on any enemy in the game as long as your character is not wearing any armor. Put some armor on, however, and the spell efficiency penalty will kick in and drop your level 25 spell to a level 24, which makes that armor penalty pretty significant for high level casters using those types of spells.
I like playing "pure" mages that wear no armor and don't use weapons other than staves. Since there is a seperate attack and casting button, a mage can switch between using charges on the staff and casting spells by just pressing different buttons. Youy can combine a weakness spell with a elemental damage staff to great effect. Staves also work well to block.
But you can also play all sorts of hybrids that use weapons and armor to varying degrees. With spellmaking, enchanting and a wide variety of spell effects to choose from, playing a mage in Oblivion can be very rewarding.