Your site must be indexed first before building links for it. You can be penalized for accumulating too much BLs (spamming) in a very short period of time.
This can happen. I have website which has not been indexed by Bing but still it shows its backlinks. It is something weird but you might have to face this kind of situation.
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For building links, checking out some of the top quality web directories as well as the article sites could be great because using both systems you can add links to your pages.
Yes, there are some scenario wherein your site has not yet indexed but already generated backlinks. As you submit your site, it will be indexed in a span of time. As well as submitting your site to directories wherein you have to wait for approval to get listed.
YOU can increase your backlinks but,your site must be indexed first before building links for it. You can be penalized for spamming in a very short period of time.
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