Learn Portuguese (Portugal): Quando o meu pai trabalha, eu estudo.

In European Portuguese, you almost always put a definite article (like o, meaning 'the') before a possessive word (like meu, meaning 'my'). So, you are literally saying 'When the my father works'.

Does the letter 'a' at the end of trabalha mean it is a feminine word?

No, verbs (action words) do not have masculine or feminine genders. Trabalha comes from the verb trabalhar (to work). For regular verbs ending in -ar, the ending -a is used for 'he', 'she', or 'it'. Here, it matches o meu pai (he).

How does the word estudo show who is studying?

Regular verbs ending in -ar, like estudar (to study), drop the -ar and add an -o when you are talking about yourself ('I'). So, estudo always means 'I study', even if you do not say the word eu ('I').

Could I drop the word eu and just say Quando o meu pai trabalha, estudo?

Yes, you can! Because the verb estudo can only mean 'I study', the word eu (I) is not strictly necessary. Portuguese speakers often drop these pronouns, but keeping it here sounds completely natural too.