1. I like "As the days passed..." also, I don't like using constructions like "he, himself; I, myself; or you, yourself. If you want to say that, you can, but put a comma between the two pronouns.
2. The word every like the word each can only modify a singular.
3. She wanted to take a biomedical course if they offer more than one.
She wanted to take the biomedical course if they offer only one.
Note the lower-case b in biomedical. Since it is the subject of the course, not the title of the course, it wouldn't be capitalized.