Learn Italian: Sto mangiando i biscotti, ne vuoi alcuni? - I am eating the biscuits, do you want some?

In Italian, when you state the quantity of a noun you just mentioned, you need the pronoun ne (meaning "of it" or "of them"). While English just says "do you want some?", Italian literally says "of them, do you want some?".

Is it strictly wrong to just say vuoi alcuni without ne?

Yes, leaving it out sounds incorrect in Italian. Whenever you use a quantity word like alcuni (some), uno (one), or molti (many) without repeating the noun itself, you must place ne before the verb to link the quantity back to the noun.

Why is alcuni used here instead of un po'?

Alcuni is used for countable things, like biscuits, and translates to "a few" or "some". You would use un po' (a bit) for uncountable things, like milk or water. Also, notice that alcuni is masculine plural to match biscotti.

I remember learning mangio for "I am eating". Why use sto mangiando?

You can use mangio, but sto mangiando emphasizes that the action is happening exactly right now. It is built using the verb stare (to stay/be) and the gerund ending -ando, which acts just like the English "-ing".