You must own the source material if you are going to do a fanedit. But this particular rule is lax for series only available on streaming services that won’t ever or aren’t planned on getting physical releases. Instead you must be paying for said streaming service to do an edit of these types of series.
As for software, a lot of people tend to use Adobe Premiere Pro or Vegas. DaVinci Resolve is also a good option if you are looking for free editing software.