I got mine through the University of Manchester. It was a study on the effects of artificial intelligence as a medium of self tuition. The only work I needed to do at the university was a competency interview (two of them) and a few days in attendance for the viva et al.
Yes, but you admit where you did it and, I'd assume, you wrote a dissertation.
Smart did neither.
In some fields you can get a degree via distance. Some you can't. If it's a field that requires people, no, you can't. This is why distance learning MBAs are utterly useless. If it's a field that requires specific research you likely can't, either. For many you need lots of time in a lab. For others, such as English, you need access to an insane amount of rare books.
Computers you absolutely can.
But again, not having that daily interaction and discourse takes a lot from it. You're less likely to learn quite as much and you'll be lacking in experience.
For some disciplines that doesn't matter as much. You're still better off not doing it at home. Always better off. From everything but a financial perspective, and you must weight accordingly.