Personally, I had a great education. My mum was a trained teacher, a Montessori teacher, and I know that I could not have written 'Eragon' if I had gone into a public school system because I would have just been too busy attending classes and doing homework - I wouldn't have had the time to write.
I find inspiration in many places. Sometimes music gives me the kernel of a story. Sometimes it's dissatisfaction with the plot of a movie or a book that gets me thinking. Sometimes it's love of a movie or book.
If you want to be a professional writer then you need to write consistently. Inspiration strikes about once every blue moon which, for me, is once every two and a half to three months, which is when I'll get really and truly inspired about something.
I think I learned most from editing, both editing myself and having someone else edit me. It's not always easy to have someone criticize your work, your baby. But if you can swallow your ego, you can really learn from the editing.
Just writing a lot doesn't necessarily make you a better writer. You have to hear yourself as a writer, and the best way to do that is to read your writing out loud.
The advantage of writing from experience is that it often provides you with details that you would never think of yourself, no matter how rich your imagination. And specificity in description is something every writer should strive for.
I had friends growing up; there were other home-schoolers we were in touch with so we weren't isolated, and I've always been happy engaged in my own projects and pursuing my own goals.