You definitely can. I started my career (15 years old) freelancing remotely. It was the perfect setup to learn and make a living. Later I got some office jobs that helped me grow faster in other aspects not technically, but the last 5 years I've been fully remote and could not ask for more. Initially my jobs were mainly local ones, currently I work for an American company and I estimate I do more $ than 99% of the software engineers in my country, even not having a diploma. I'd call it a success.
I think you could. The hardest part would be the first five years, when I think you benefit from in person learning the most. But if you found a good shop that was 100% remote and could support newer developers, I think you'd do fine.
Yes. And it is becoming increaslying easier with the amount of companies that are moving to remote working.