Ы on its own deserves a special article, so I didn't want to tackle it. By the way, your only problem in my opinion is that you reduce the unstressed syllables too much! Don't overdo it, and you'll sound perfectly natural ;)

Elizabeth:

Actually not far. At least comparing to English. If you say russian words as they are written, native speaker will always understand you. Of course, there are exceptions, but in common there is no such a huge mismatch as in English.

Interesting, I don't think I knew even half of those rules! But then I do use the approach suggested at the end, which is to listen and then try to immitate.

I would add another common error, and that is the pronunction of И and Ы, with the latter being often pronounced the same as the first. I certainly suffered from that one until it was pointed out to me, thankfully fairly early on. That's where the explanations come in handy, they help you to hear the things that perhaps you didn't notice before.