No, this is an EF-S lens designed specifically for Canon APS-C sensor cameras. It will not mount on full-frame bodies like the 5D or 6D series.
Yes, the built-in 4-stop Image Stabilizer (IS) helps significantly in reducing camera shake during handheld video recording.
The Canon EF-S 18-55mm f/3.5-5.6 IS II uses a 58mm front filter thread.