I tried to speedrun Super Mario Bros 3 warpless. After I beat Browser, I test my video. I saw that Mario stays in the map doing anything else, than I saw when I was playing. I don't know how to fix it.
Is that possible to use video capture with Windows 10 (Windows + G), or is that forbidden?
Not really clear what you're asking. You say that your video capture has recorded something else than what really happened? If so, what is the difference? Doesn't seem like it's related to smb3 or the emulator, but an issue with your screen recording program; although I think we need more information.
There aren't any restrictions on video recording software, you can use whatever works for you. I would recommend trying OBS, it's easy to use and configure.
I recorded with the record feature of Nestopia 1.40. I played my speedrun without any problems. But, when I play the video, something else happens. Mario stays on the map for at least 1 hour. So my speedrun is ruined.
I used the same emulator for my Super Mario Bros speedruns, and that works fine.
Did a quick Google search for "Nestopia 1.40 recording" and found that a few users reported broken recordings on certain games, it's possible this is happening here. Not sure if there's anything you can do within Nestopia to help, but you can always use an external program (OBS) to record or just use a different emulator.