I have on my smartphone a VPN (NordVPN) in itself everything works great. But I wanted to stream Netflix on my TV (with a Chromecast), so the question is, can I do that? I'm on my phone so it should not be a problem that I watch American TV series. It works so synonymous or does the vpn no longer work there?
The Chromecast will most likely use the router's router (W-LAN) and not your cellphone's with VPN. Many routers offer the possibility to set up a VPN directly in the router configuration.
Router → Mobile → VPN → Netflix
Router → Chromecast → Netflix