No, this is an EF-S lens designed specifically for APS-C sensor cameras. It will not mount on full-frame Canon DSLRs and may cause damage if forced.
Yes, the built-in 4-stop Image Stabilization is highly effective for handheld video, though the autofocus motor may be audible on internal microphones.
On a Canon APS-C body, the 1.6x crop factor gives this lens an effective focal range of approximately 28.8-320mm.