Am I allowed to pass unequipped weapons (or items) to any survivor?
There are two types of moves that involve giving cards to other players.  They are Hand Off and Request.  The one you probably want is request.


  Request: During his turn a player may request 1 or more item cards from other players. Other players may give the requesting player an item card from their hand, if they do, that card must be revealed and immediately played. The requested card cannot be added to the crisis.


Request allows a player, on his turn, to get cards from other players as long as he plays it immediately.  I'm presuming that the card you want to give to someone is unequipped so in your hand.


  Hand Off: During his turn a player may have a survivor he controls that has an item equipped hand that item off to another survivor at the same location. When an item is handed off it is unequipped from the survivor that is handing it off and is immediately equipped to the survivor that it is being handed to.


Hand off is basically if a survivor already has an item equipped (i.e. it is "in play" and out of your godly control to move around to other survivors without restriction), then he or she can give the item to another survivor in the same location.

So, yes, you can pass that unequipped card but not on your turn.  You have to wait until that player's turn before they can request it from you to place on that survivor.