I am a greencard holder who has moved back to Europe and will give up my GC. Can I open and operate stock trading accounts in US to manage the money I made in the US?
Why give up the GC? That ought to be an interesting story.
Not OP. It gets tricky to hold on to it if you're not in the country for at least 6 months a year.
Not the OP, but you need to reside for at least 183 days a year to keep your immigration status.
Green cards come with residency and physical presence requirements. Leaving the US for more than 6 months gets complicated. Making frequent trips back to appear to be a resident will eventually be called out.