Learn Farsi: بعضی از مهمان‌ها جوان هستند.

Yes, you can! Ba'zi az translates literally to 'some of', while ba'zi-e just means 'some'. Both are correct and widely used in everyday Farsi, though ba'zi az is great for emphasizing that you are talking about a specific portion of a larger group.

Since ba'zi (some) already implies more than one, does the noun mehman (guest) have to be plural?

Yes, it does. When you use ba'zi az (some of), the noun that follows must be plural, which is why we add the plural suffix -ha to make mehman-ha (guests). This works just like English where we say 'some of the guests', not 'some of the guest'.

Why does the adjective javan (young) stay singular when the guests are plural?

In Farsi, predicate adjectives (adjectives that describe the subject and come right before the 'to be' verb) do not get a plural ending to match the subject. You just use the base form of the adjective. So it is always javan هستند, never javan-ha هستند.

Why do we use the plural verb hastand (are) here?

Because the subject is a plural group of people (mehman-ha). In Farsi, plural human subjects must take a plural verb. As a quick reminder from earlier lessons: if the subject were plural inanimate objects or animals, you would usually use a singular verb instead!