Can you transport PDS in ships like in TI 3?
No, PDS are now locked to their planet. However, if all of your PDS are out, you can build a new one by removing an old one from the board.
When you use the secondary ability of construction can you place it on a system already activated (that means placing a second command counter on the system) ?
Yes, you can, but the 2nd command counter goes to your reinforcements. You never place a 2nd command counter in a system.