My Ning site has the keywords in the URL, lots of good content, decent activity, some inbound links and time on the internet. However, I don't show up for my key words (deadliest catch) until page 9 in Google search results. This should not be the case.
The most important single element in terms of search results positioning is quality backlinks. It looks like you currently have backlinks from 14 different domains. The relative page rank of those sites determines your position, so increasing the number of high quality backlinks should improve your positioning over time. You may want to also have 'Deadliest Catch' or other important keywords in your network description since this may help set the correct context for searching. Right now you're on the first page of results for "deadliest catch fans" and moving that up to the top of the results might be a good short term plan that will improve your overall standing as well. In terms of moving your network to its own domain, initially you will be starting over in terms of results, though using the domain forwarding tool will help here. Generally speaking, moving your network to your own domain won't likely in itself have any effect on your results positioning.
That really depends on your audience and their expectations, but I suspect that many NCs would say that it does. In terms of pagerank, when you use your own domain, you are building up pagerank on your own domain rather than on Ning's, and you have greater flexibility in pointing other services, like a blog, to subdomains etc.