By the "A figure is friendly to itself" principle in the RRG, can the Imperial Officer use his ability to obtain double movement point or double attacks (in the case of the elite IO)?

No, order and executive order require “another” friendly figure.

Also, a figure can just perform two Move actions per activation to gain 2x movement points.

Furthermore, double movement points would make no sense at all. You use the Officer's first action to perform a move. Then you would use his second action to order himself to move (if that was allowed). Instead he could just use his second action to just perform a second move. What would be the benefit of ordering himself to move instead of just move?

I see a theoretical benefit of shooting first and then ordering himself to shoot again. But in reality you'd rather order someone with a stronger attack (about any other imperial figure) to attack.