Avi->mp4->dvd, Quality question

[msdivine]

Hello,
I am using Nero Vision and have a few questions.

1) If I convert AVI to MP4, is their a loss of video quality. Or is it the same. The reason is that I would like to store my AVI's and since they take up so much space, I thought MP4 would have no loss of quality.
If there is a loss of quality does anybody know of the specs.

2) If I convert AVI to DVD (To play film on DVD), is there a loss of quality?

3) If I convert DVD files to MP4, is there a loss of quality.

Please advise,
Ms. Divine