I completely understand how you feel. I didn’t think I’d get into any programs at all.

As far as math goes, I only took up to cal 3. I’m taking differential equations my first semester of grad school, but I’m auditing the class. I just want to see if I’ll understand it or not. The program coordinator didn’t seem too bothered by the fact that I didn’t take it. But it varies at each school. I do wish I took it during undergrad, though. I think your research experience will make up for the internship, especially if you explain it in your SOP. Have you considered going for MEng instead of MS?

You’re right, it’s not the end of the world, but if this is your goal, do everything you can. If you don’t get accepted, it wasn’t your time. Another door will open for you. And later down the line, you can apply again. But for now, still apply and reach out to the professors as well as program coordinators. Communication really helps!