Learn Portuguese (Portugal): Eles estudam na terça-feira e na quarta-feira.

In Portuguese, to say that you do something 'on' a certain day, you use the preposition em. Since days of the week from Monday to Friday are feminine nouns, em combines with the feminine word for 'the' (a) to form na. You are literally saying 'in the Tuesday'.

Why is na repeated before both days? Could I just say na terça-feira e quarta-feira?

It is standard in Portuguese grammar to repeat the preposition and article (like na) before each item in a list. Repeating it before quarta-feira sounds much more natural to native speakers than leaving it out.

Do I always have to say the -feira part for Tuesday and Wednesday?

In everyday spoken Portuguese, people often drop -feira and just say terça and quarta. However, it is perfectly correct to include it, and beginners are usually taught the full words first so they know the official names.

Why aren't terça-feira and quarta-feira capitalized?

Unlike in English, days of the week, months, and seasons are written with lowercase letters in Portuguese unless they appear at the very beginning of a sentence.