Thanks for the question!
Would you mind posting a link to your site here? Or at least PM it to me...
First question - Yahoo really does often give out backlinks when Google does not. You can always go to Google and check how many links there are to your site using the link:yoursite.com operator.
Also please take a look at the video where Matt Cutts explains why Google returns very few backlinks:
http://www.youtube.com/watch?v=TjQ2QVQpaK0Try adding Blekko to your project - that new search engine usually returns a lot of data.
Second question — the links might be there and already indexed by Google, but still not appear in the backlink list that the search engine returns. Eventually these backlinks will appear in your project as you rebuild it. For now you can create a new project using these links via File -> New Project (Expert Options) -> Enter backlinks manually. Or, if you have LinkAssistant, you can create a project for your site and paste those links as "partners" to verify them and calculate their value.