1. It will help all areas of your pronunciation, some of which would otherwise be hard to train. Even if you can pronounce the whole syllabary flawlessly, there's no saying you can produce sentences with the flow and finesse of a native speaker.
2. It depends if you can understand them. If you know exactly what the sentence means, does it matter that you haven't learnt the grammar separately? It will actually make life a lot easier when you do come to study it.
3. I think if they're that bad, you should look for something more natural. Try using JPod's dialogue only track or something. If you're studying the lessons, it would make sense to shadow them.
That said, I did a lot of shadowing but still had some fairly fundamental flaws in my pronunciation. I think there's value in repeating individual words until you get them exactly right as well. You might need a teacher/friend to confirm this though. Check Jim Breen's dictionary for audio files. You might also find
this video useful. I doubt you'll be able to understand the Japanese, but she's explaining how to enunciate vowels correctly, so try comparing with your own pronunciation.