Learn Farsi: پروژه دیگر منظم است. - The other project is organized.

In Farsi, the ezafe linking a noun to its adjective is rarely written out. Because prože ends in a silent 'h' (which makes a spoken 'e' sound), the ezafe takes the form of a 'ye' sound. You must pronounce it as prože-ye digar to properly connect the two words.

Since this lesson covers plural demonstratives like inhâ (these), how would I say 'These are organized' versus 'These projects are organized'?

If you just want to say 'These are organized' using a pronoun, you use the plural: inhâ monazzam hastand. However, when you include the noun ('These projects'), the demonstrative must stay singular while the noun becomes plural: in prože-hâ monazzam hastand. This is a very common rule to remember at this level!

I've heard people say dige instead of digar. Can I use that here?

Yes! digar is the formal, written form of 'other'. In conversational spoken Farsi, it is almost always pronounced as dige. In a casual setting, you would say prože-ye dige.

How does the verb ast (is) change in everyday spoken Farsi for this sentence?

In casual spoken Farsi, ast usually shrinks to just an -e sound attached to the end of the previous word. A native speaker would casually pronounce this entire sentence as prože-ye dige monazzam e.