They do not require it here, but the article is required in English here.

Yes 'o' is fată and 'un' for băiat.

I am not very sure, but I think this works mostly with human-related things, such as: man, woman, girl, boy, teacher, worker, engineer etc.

This course was created by Romanian/English speakers. They might not speak how you speak, but they know Romanian.

If you see something incorrect, report it.

yes it does not sound correct. I was also born In one too