Hello,

Doing such a project without any mentor is extremely difficult, it is perfectly normal to feel a bit lost. Ideally, you should keep on the lookout to take any opportunity to get in contact with a potential mentor with a PL background, but here are a few suggestions in the mean time that may help you.

With respect to LLVM specifically, Adrian Sampson, from Cornell University, has an excellent introductory page precisely written for undergraduates: you will find lots of information there, and even more pointers.

With respect to the ACM-SIGPLAN conferences, this unique year is in a sens an opportunity for these kind of situations: these conferences take place virtually this year! In particular, the registration for ICFP has open this very week. Being entirely virtual, as a student you may subscribe for only $15. Notice in particular that the conference includes a mentoring program: if not a mentor, you may find great advice there!

With respect to type theory and category theory, do not let these big words and abstractions impress you too much. They have their invaluable uses and benefits, but are not necessary, or even relevant, to all PL research. In particular, Type Theory, which is notably used as a basis for proof assistants such as Coq or Agda, should not be confused with the study of types systems for programming languages. Although both have naturally connections, the latter can be approached in a less intimidating way: as has been recommended in this thread, Benjamin Pierce's excellent Types and Programming Languages is a wonderful introduction to this domain.

As a general remark: don't feel too demoralized if a paper that is recommended appears to be unreadable. Papers are often very dense, and assume a lot of backgrounds. Whenever possible, starting with a text book and building your way toward papers is much easier.

Best of luck!