Can I use Junk Arm, discarding something + 1 Item card to get that 1 Item card back into my hand?
No, you cannot return cards to your hand that you used to pay this card's cost.
Source: PUI Rules Team (2011-11-03), TPCi Rules Team (2013-02-07)
When the Junk Arm trainer says "you can't choose Junk Arm", does it mean any Junk Arm already in the Discard Pile, or just this specific card?
It means you can't get any Junk Arm cards from the Discard Pile.
Source: Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)
Can I use Junk Arm if there aren't any trainer cards already in the Discard Pile?
No, you cannot play Junk Arm unless there is at least one Trainer card other than Junk Arm already in the Discard Pile beforehand.
Source: PUI Rules Team (2010-12-09), PUI Rules Team (2004-06-16)