is there any method to cut part of 360 video and convert it to plain video? I want to take half, or less of 360 footage and then edit/view as plain one.
Yes, I believe the latest versions of Premiere CC can do this natively. It's a little bit tricky since the video needs to be unwrapped, but it is a fixed distortion to be applied depending on the size of the sphere map. 360 videos are actually rectangular videos that are texture mapped on to a sphere.
Software that wants to convert can either look at the size of the sphere and use a fixed distortion to get the correct output or actually execute the spherical mapping and then shoot a flat image of the mapping in a 3d translation. The later approach is more complicated by a bit, but allows for easy manipulation of the camera within the 360 sphere.
I'm not particularly aware of any other applications that directly support working with 360 video yet. I know Fusion has VR capabilities now, but have not had a chance to work with the new features yet.
Pinnacle Studio should be able to do this in the latest version, in Ultimate edition: https://www.pinnaclesys.com/en/landing/360video/#convert-360