Thanks so much for the tips!
I've reached out to some of the people copying parts of my site to try to get them to take down the duplicate content. It kinda stinks when that's out of your control and it hurts you, but I completely understand why the search engines do it.
I haven't done any intentional link building. We occasionally will put out a popular blog post or a news story will get written about us, so if you are seeing an increase in links during a specific time it was likely just that.
Thanks again for the great info!!