Hi. If a mage who is astral projecting and is doing overwatch for a SR group infilitrating a building then can the astrally projected cast spells against people in the physical world??

Combat would be a good example of this. If the mage cast a stun ball or elemental manipulation spell to effect people in the physical world then would the spell(s) work against physical objects/people??

No, a mage can only cast on things in the same plane as himself. An astrally projecting mage can only affect astral beings, or dual-natured beings.

An astrally projecting magician can't even Conjure spirits, either, IIRC (as both Projecting and Conjuring are deemed Exclusive actions)

Correct. You can, however, give commands to spirits while projecting. You cannot summon or call from stand-by any spirit, but if they were around before you project, you can give them orders normally.

Yeah.

Since an astrally projecting magician is pretty useless on the physical realm, I've found an Ally Spirit performs this task well -since it can not only perform astral overwatc, but in a pinch it can materialize and provide additional support on the physical realm.

Summoning (when one first conjures) is exclusive, but calling or commanding a spirit is not exclusive, and so both can be done while projecting.

SR3, p.186

So, in other words. If my mage character wants to help protect the SR runners in my group through astral projection then I will have to summon some spirits (elementals in my case since I am a hermetic mage and not a shaman) to do combat for me.

The only exception is using spells against any astrally perceiving or dual-natured creatures if I get that lucky.

And when a mage cast spells in the astral, that mage takes physical damage instead of stun.