Panasonic Lumix G Vario 14-45 with E-M5 and E-PL1

I have some questions for those who have experience with Panasonic 14-15 with E-M5 and E-PL1

Will Pana lens stabilization work with E-PL1?

Will be E-PL1 in camera distortion correction work with Pana 14-45 same way as with Oly lenses?

Will be AF same quick as with Olympus lenses? I had Panasonic 20 and it was terribly slow with E-PL1 so is 14-45 better with E-PL1 than 20 idealy same as Oly 14-42 II?

Thx