Learn Romanian: Tu scrii numărul lor? - Are you writing their number?

In Romanian, possessive words like lor (their) almost always need to follow a noun that has a definite article attached to the end of it. So, you cannot just say număr lor (number their); you have to say numărul lor (literally "the number their").

If "you" were writing down multiple numbers instead of just one, would lor change?

No, it wouldn't! That is because lor is an invariable possessive pronoun. While words for "my" or "your" change to match the gender and quantity of the item owned, lor (their) stays exactly the same no matter what. "Their numbers" would be numerele lor.

Why does scrii have a double "i" at the end?

The dictionary form of the verb "to write" is a scrie, and its base stem is scri-. To make the "you" (tu) form, we add the standard -i ending to that stem, which gives us scrii. You pronounce it by slightly stretching out the "ee" sound at the end.

The English translation asks "Are you writing", but there is no word for "are" or "do" here. How is this a question?

Romanian doesn't use helper verbs like "do" or "are" to ask questions, and you don't need to change the word order. You simply take the normal statement for "You are writing their number" and raise the pitch of your voice at the end to make it a question.