The university keeps track of how many copies of lecture notes each professor has sold. Each lecture is taught by a different professor and uses distinct lecture notes. Here is the sample database relation SALE:

Identify all the functional dependencies present in the SALE relation based on the database model.

Determine a suitable primary key for the SALE relation and provide an explanation.

Normalize the relational schema into Second Normal Form $(2$NF$),$ ensuring proper organization of attributes and data.

Normalize the relational schema into Third Normal Form $(3$NF$),$ eliminating any transitive dependencies and ensuring data integrity.