I will to answer your first question:
Does a degree in Web Design make a possible candidate for a position more attractive or is it based on their portfolio?
If I was planning to employ a web designer, I would have very little interest in whether or not they had a degree. The main thing I would want to see is one or more sites they had actually designed. So, with that in mind, the portfolio is vastly more important than any formal qualifications. Of course, other prospective employers or clients might take a different view, but I think my approach would be fairly typical.
Also, it seems to me that, if you are thinking of a full-time university course, that's going to take three or four years, and it's going to cost a lot of money. That's a big investment to learn something that a competent person should be able to learn in a matter of weeks or months. Consider too that by the time you had finished the course, the technology will have changed, so your skills might be out of date before you even start work.
The great thing about web design is that you can actually do it as you learn. There's nothing stopping you from starting a web site today, and gradually developing and enhancing it as your skills improve. Your first shot might be rubbish, but you can then do another one. And then perhaps another one after that. Before you know it, you have a portfolio - something to show prospective employers or clients. (You can't do that if you want to train to be a civil engineer or a dentist or an airline pilot.)
You say you've already done 12 months self-study. On that basis, you ought to be ready now to start developing a portfolio - and looking for work. If you are not, maybe you just need a bit of direction in your study programme. But if you've spent 12 months trying learn the subject but are no closer than the day you started, that suggests you should re-think your choice of career.