2. Only mana spells, foci, and astral attacks can harm astral forms according to the books we have. Is there any other way that a mundane character can harm a astral projecting spirit or mage?Attack of Will. Street Magic pg. 94
Arguably, "no". If you're talking about a materialized
spirit, then yes, Attack of Will is applicable. However, if you are talking about, as the OP says an "astral[ly] projecting [...] mage" (A spirit doesn't "astrally project", they're native to the astral & already there), NO. Mundane characters and creatures have zero access to the astral plane, therefore they aren't on
the astral plane to harm an astrally projecting mage (or non-materialized spirit).
Please note, that a materialized spirit is subject to damage from mundane attacks, if they can overcome the insane hardened armor (Force x 2) granted by Immunity to Normal Weapons. Stick-n'-Shock is probably your best bet (reduces that armor to Force, much more manageable) if you can't afford a flame-thrower. APDS is another expensive solution, but if you're just starting, spirits above Force 6 should be incredibly rare (and not fought), so AP -4 is close enough to AP -half.
Additionally, if that spirit is materialized, the mundanes can start wailing away with Attacks of Will (as voydangel suggested), but if they don't have some impressive Charisma or Willpower, they're better off with elemental normal weapons (-half is a good thing).