Does Antimagic Aura affect the caster?

Quote from Sequilonis >>

And an Emanation can not reach into the field at all because an Emanation originate at the caster and extend in straight lines outward in all directions, so the Antimagic Field would stop the Emanation at the edge of the field in the same way a solid wall would.

This applies the projectiles too.

Quote from Sequilonis >>

 Except the spell does not say that spells "can't reach through" the effect. If a spell doesn't say it does something, it doesn't. 

So you agree, the spell doesn't say that a projectile can reach through the effect.

An AoE type effect "can't extend into" the aura and thus cannot extend "through" the aura.  But an ongoing AoE that can be moved, such as Spirit Guardians is merely "suppressed" while in the field.  For example, someone could target himself with Spirit Guardians while outside of the aura, then walk through the aura and out the other side of it and at that point the Spirit Guardians spell would be functioning as normal.

Spells which are not AoE spells and are designed to directly target a creature within a specified Range are only restricted by where the spell is cast and where the target is located.  The Range of such spells determines where the effect originates.  Even a spell like Magic Missile, regardless of its flavor, has its effect created at the target creature's location.  So, if two spellcasters are facing each other with an antimagic aura located between them, but neither of these spellcasters is actually located within the aura, then the first spellcaster can cast Magic Missile and target the second spellcaster with that spell, and the second spellcaster can cast Magic Missile and target the first spellcaster with that spell.  There is nothing within the text of the Antimagic Field spell which prevents this.