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#1. Can a magic user in close combat cast a spell as long as it is not a magic missile or states otherwise.
A spell can be cast FROM close combat at will, the only exception is Magic Missiles which specifically prevent this. However, be aware of Line of Sight. Typically if your Wizard is in close combat, they wont have Line of Sight to any enemies (or friendlies) except the enemies they are in combat with. At this point, you have to see if the spell allows you to cast AT units that are in close combat. The spell description must specifically state that it can be cast AT units in combat. Please make sure to notice the difference between casting FROM combat and casting AT combat. Warhammer Fantasy Rulebook page 107, Casting Spells paragraph 6.
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#2. Can a normal magic user wear any type of armor and still cast spells.
The Engineer is correct on this one. A model may only purchase Magical Armor if they are allowed to wield normal armor first. The vast majority of Wizards cannot use armor and therefore are not eligible for Magic Armor. Chaos Sorcerers being the primary exception to this rule. Warhammer Fantasy Rulebook page 121, Magic Armor paragraph 3.
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Although there is a spell in the Daemons Nurgle list that doesn't say can be cast in combat but reduces anyone in base to bases stats..kinda pointless if you don't cast it into combat.
Miasma of Pestilence targets the caster and therefore can be cast in combat. Daemons of Chaos 7th Ed FAQ, Daemonic Magic question 2.