At least we are on agreement on something.
You can cast spells from within a globe of invulnerability, but any effect that intersects the globe is suppressed. Thus, mirror image and prayer would be suppressed on the caster, although prayer would function on others once they left the globe.
Globe of invulnerability states that the area of effect of certain levels of spells does not include the area of the globe. In 3.0, this made it impossible for a wizard to buff herself and nearby allies without making the buffs useless. In 3.5, this was fixed by this, "Spells of 4th level and higher are not affected by the globe, nor are spells already in efect when the globe is cast." (emphasis mine). This way, a wizard can buff herself all she wants, and the spells will function as long as she casts GoI after the buffs.

You can cast spells from within a globe of invulnerability, but any effect that intersects the globe is suppressed. Thus, mirror image and prayer would be suppressed on the caster, although prayer would function on others once they left the globe.
Globe of invulnerability states that the area of effect of certain levels of spells does not include the area of the globe. In 3.0, this made it impossible for a wizard to buff herself and nearby allies without making the buffs useless. In 3.5, this was fixed by this, "Spells of 4th level and higher are not affected by the globe, nor are spells already in efect when the globe is cast." (emphasis mine). This way, a wizard can buff herself all she wants, and the spells will function as long as she casts GoI after the buffs.