What are the formal terms such as dictionary shape, なぃ shape, ます shape and ば shape in the study of college Japanese majors?

Dictionary form is what we call prototype, also called basic form, such as book;

なぃぃぃぃぃぃぇば; Booking か +なぃ

ますすすすぇすすすすすぇすすすす.

ばば is also called imaginary shape, such as ぇば and けば.

In addition, in some grammar books, we usually say the latter form

なぃ is a part of the book, excluding なぃ;

The book き is the shape of ます, and the book きます is just a title of respect for the book く;

Book け is its hypothetical form, and it does not contain ば.

I hope it helps you. You can also ask what is not enough.