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...do these links inside the iframe count as inbound links to my page for Google?
Will I gain pagerank from these links?
Yes, but probably not much. The amount depends on the inbound links to the iframe.
Iframes are not an efficient way to distribute PageRank or a good way to distribute link reputation, because they themselves are not liable to get inbound links, or have content that provides good surrounding context for the links.
They're actually more useful for links that you don't want to share a lot of PageRank.