If a character using the gauntlet+space gem and the underworld TA, can he carry 2 pieces; 1 without the underworld using carry ability granted by the gem, and 1 with using the TA?

Memory serves, you can't be given multiples of any power save for Perplex (Which, if you want to be technical, just modifies by multiples instead of being multiple +1s or -1s.).

Nope, cuz no matter what, the Underworld TA specifies that to carry 2 people, they must both have the TA.

I'm not sure where you are getting that you can be given multiples of Perplex. You cannot. Multiple people with Perplex can give you a modifiers, but that's not the same thing as having multiples of Perplex.