Feinting with Push
 

Actual table question: Can the Push skill be used to Feint?

On the actual rules side, Unarmed Combat Skill is not actually defined anywhere, but Push is stated to make an unarmed attack. I'm tempted to ask "could Push deliver a touch spell?", because Adventurers calls out unarmed combat skill specifically on that topic. Not to be accidentally helpful, Spells says you need a standard melee attack, a term which unsurprisingly appears nowhere else, but the “try to wrench your staff away as your attack” option lets me believe the expression means "a melee attack which is not a new special type because of a melee spell is involved".

As for what the answer should be, it would surprise me that a thing that can send someone flying across the room and can be parried, blocked or dodged could not be used to threaten to send someone flying across the room in order to divert their parry, block or dodge.

Re: Feinting with Push
 

I can't think of any exception to the statement that an Unarmed Combat Skill is used to make an unarmed attack. I believe Push is definitely applicable for a feint.
I don't know that I'd allow an unarmed combat skill that can't be used to defend to be used to defend against a feint. On my table I'd rule the skill you resist Feint with must have a parry or block available to it.

Re: Feinting with Push
 

Push is just a highly specialized unarmed combat skill with steep prerequisites and a single purpose (shoves). You can safely treat it as being just like Karate as far as feinting, resisting feints, delivering touches, etc. go. You just can't use it for any attack but a shove.