2013 Macbook Pro 13" - Running 2 monitors (not thunderbolt) Can I run 2 non thunderbolt monitors off a 2013 13" Retina Macbook Pro? One connected via HDMI, and one connected via a Thunderbolt to HDMI adaptor?

And if so, can I also run the laptop screen at the same time?
Yes, what you're suggesting will definitely work and you can use all three displays at once (MacBook display + HDMI display + Thunderbolt/HDMI display). This is the Mini DisplayPort to HDMI adapter that I personally use and recommend.