Maybe. The technology that is used isn't foolproof.
I've never had a problem casting from a Chrome browser to a Roku on either Windows or Mac. But I've never tried anything else, because I have neither needed nor wanted to, so I can't offer anything beyond that. But casting video from a Chrome browser to Roku has always worked well for me.
Lots of people have reported inability to mirror Windows to Roku, but that's generally because the computer doesn't have the proper hardware or drivers to make it happen smoothly. Again, something I've never tried.
If you gave specific examples of what it is you're wanting to do -- your wording is very general, as my answer only covers a part of it -- then those that have tried the same can offer good advice.
... I'm an expat, living in a new country. I looked at Roku a few years ago, my recollection is that it required having a tv back in my home country. Is there any requirement like that now?
Never heard of such a requirement in my dozen years of using Roku. Of course, I'm in the USA where we don't have TV fees (UK calls them TV License) that some countries have.
Now, for what you didn't ask. If you are outside one of the 17 supported regions (go to Roku Website and scroll to the bottom, click the country, and see the list), there's a good chance some apps won't work. It doesn't matter if the service works on other platforms. If the developer does not make the Roku app available outside Roku supported regions, the app won't work.
DBDukes Roku Community Streaming Expert Note: I am not a Roku employee.
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