Late followup for Internship Opportunity About a week and a half ago I received an email from a mentor with whom I'd previously inquired about internship opportunities, informing me of possible projects I could join. I accidentally let it slip for a bit and responded after 4 days. It's been almost a week since - how should I go about following up? I'm really punching myself in the gut, this was perhaps my "dream" work per se.
Simple enough to just ask. Ask if the offer is still open and what your next steps should be. And express your enthusiasm as you have here. 

Four days isn't actually that long. Nor is a week without a reply. But if it is upcoming soon then an email now should be fine.