Questions & Answers about Băiatul are numărul ei.
Why does numărul have the -ul ending if the English translation is just "her number" and not "the number"?
In Romanian, when you use a possessive word like ei (her) after a noun, that noun almost always needs a definite article (the equivalent of "the"). So, you literally say "the number her" (numărul ei). The -ul at the end of numărul is that "the" attached to the noun.
Does the word ei change depending on the gender of the object being owned?
No! Unlike words for my, your, or our, which change to match the noun being owned, the 3rd person possessives (lui for his, ei for her, lor for their) are invariable. The word ei stays exactly the same whether the object owned is masculine, feminine, or plural. It only tells us that the owner is female.
Since numărul ends in -ul like băiatul, does that mean it is a masculine noun?
How would the sentence change if the boy had "his" number instead of "her" number?
You would say Băiatul are numărul lui. You just swap out ei (her) for lui (his). Just like ei, lui is invariable and doesn't change based on the word numărul.