If my Transporter were to move or make a transporter attack, can he pick someone up om the way?

Only if the piece they are picking up is adjacent to the transporter at the beginning of the transporter action.

And the passenger cannot be put down until after the move ends. Which means, he will not be on the map when the attack is made, so you cannot use any powers or TAs the passenger might have during the attack. He gets placed adjacent to the transporter when the move ends.

What about Shield/ enhancement with transporter carried move and attack power?

mmm brains

See Funky Jett's post above. Doesn't matter what the power/TA/feat/whatever is, if the character is carried during a Transporter move and attack, it is off the board during the attack.