Your character must be male for the Handmaiden to join you after leave Telos. If you have a bit of influece over the robot, you are able to have him make computer spikes for you. The last time will give you the ability to heal droids through the force. You can upgrade him a total of four times.
This will also depend on your computer, intelligence, and repair skills. If you gain enough influence with T3 you will have the option to permanently upgrade his capabilities. He can even be sold for scrap on Nar Shaddaa, although he will return later in the game. If you are looking to be evil, abuse T3 at every opportunity. This will usually entail choosing the lighter side of a conversation.
Influence Keeping T3 on your side involves speaking kindly to him. Droids are useful for' ranged combat and immunity to force powers. If you choose to play the prologue (or have play' ed the first game) you will become famliar with T3 quickly.