guess it depends on your definition of backlink. any link that is not on your own hosted domain that points to your sites and works is a backlink.
I heard from people that if you put your new site that hasn't been indexed yet on your dp signature. You could get indexed onto google within a day or two, is that true?
You should also submit your not-yet-indexed sites to dmoz and various other directories, as well as do some light blog commenting on sites with higher PR.
Yes the links are not set to nofollow, making the dofollow. Also putting a non-indexed site will most likely help you get indexed in my opinion. Click on settings on the top of the page.
Signatures and live links within posts are not available to users until they have been a member at least 7 days, have positive (green) reputation and have at least 10 posts.
All DP signature is do-follow and they are highly effective. Not only in getting link but also for traffic if you put your signature in highly attractive way.
No follow links are still important to get. It is advisable to not just go for do follow links all the time as the backlinks need to look natural...
Yes, the DP signature is a backlink because DP is a do follow attribute wherein those backlinks can be recognized.