Learn Italian: Io sono l'insegnante e tu sei lo studente. - I am the teacher and you are the student.

You are right! Usually, you can drop them because the verbs (sono and sei) already tell us who is doing the action. But here they are included to create a strong contrast between who 'I' am and who 'you' are.

Why is it lo studente and not il studente?

Most masculine words use il for 'the'. But when a masculine word starts with an 's' followed by another consonant (like the 'st' in studente), it must take lo instead. This makes it flow better when speaking.

Why does insegnante get l' as its article?

Because insegnante starts with a vowel. Whether the word is masculine or feminine, if it is singular and starts with a vowel, the words for 'the' drop their vowel and become l'. It joins directly to the word to make pronunciation smoother.

Could the conjunction e ever change spelling in other sentences?

Yes! In this sentence, it stays e because the next word (tu) starts with a consonant. But if the next word started with a vowel (especially another 'e'), it would often change to ed to make it easier to say out loud.