I am looking at dictionaries of the avesta and old persian of which there isn't much, and would like to collect words in the old persian cuneiform and avestan script. First part of the question is, how different are the Avestan Language, Old Persian/Iranian, and Farsi? Second part is, would it be acceptable to take a Farsi word and render it using Old Persian Cuneiform? Or render it in Avestan script? I ask because I would like to write in these languages and there isn't much in terms of dictionary, so wondering if I could use Farsi words to write in it. Or is it like Old-English to Modern English?
Your first question: Avestan and Old Persian are the two attested Old Iranian languages. Both are very close to the reconstructed Old Iranian, and thus to one another. New Persian (Fārsī) is (mainly) descended from Old Persian, but it has moved very far from Old Iranian.
Your second question: The Zoroastrians in Iran and India do sometimes write New Persian texts in Avestan script, though not very often. It seems that no one has tried to write New Persian in Old Persian cuneiform script, but in principle you could do so if you really want to.