Do Urdu Numerals belong to the Persian Script and does Urdu use the same Unicode characters as Persian Language apart from Western Arabic numerals?
About Numerals, yes! Since those numerals belongs to Persian language, they are the same and even the same with Arabic except that number 4 number in Arabic which is different. Each one of these three language are in addition to be a separate language -especially about Arabic which is completely from a different language family- In written part there are several completely different characters which don't exist in the other one. (and of course Persian is not written with Arabic script, instead, Arabic is written with Persian script, There are some documentation that illustrate why (it's another topic...) look at this examples:
Urdu: In Urdu in additional to Persian letters there are 4 characters that in Persian don't exist: ے , ں, ڑ, ڈ Persian: In Persian there are 4 characters that in Arabic don't exist: پ ، ژ ، گ، چ
So it's Urdu > Persian > Arabic. And because even those similar Urdu characters often can't be understood either among Persian or Arabic people. you have to install each Unicode and language differently. I'm native Persian and speak and understand mostly Arabic and Urdu because of my studies.