What factors do I consider before deciding to ask my summer research guide for a recommendation for grad school?
I am unable to decide if I should be asking this professor for a letter of recommendation


Of course you should be asking!

Specifically, you should be asking whether this professor is willing to write you a strong letter of recommendation. The word “strong” (or a similar synonym) is crucial here. You want to make it clear that a weak letter may do more harm than good, and you’d much rather receive honest negative feedback now, face to face, while you still have some time to improve, than to risk spoiling your application.

Stop trying to read the professor’s mind.  Stop trying to imagine all the impostor-syndrome-inspired weaknesses that the professor could write about. Every applicant has weaknesses.  Just ask.


  unsure of whether this is something that I'm good enough to do


Do not listen to the Impostor Syndrome. There is no such thing as being good enough; what matters is what you do.

And what you are doing is pursuing an internship that addresses the gaps you perceive in your own background. You see a gap in formal CS preparation (even though that preparation is rare among programmers, and even rarer among physics students), but you are addressing it by learning to program anyway. You see gaps in your mathematical background, but you are pursuing a mathematics internship that requires you to do a lot of independent study.  You are deliberately working outside your comfort zone to strengthen your background—of course you feel overwhelmed!

In short, you’re acting exactly like a researcher.

I agree with Buffy. From out here, it looks like you’ll be fine. Keep up the good work!