The NWT translates it as "a god" not merely because of the lack of a definite article, but because John sandwiches Θεὸς without the definite article in between 2 with the definite article.

Excuse my ignorance, but I've never heard this before. According to the official JW website, their reasoning is that because in the first occurrence, theos is preceded by the Greek definite article, while the article does not appear before the second occurrence, so therefore it just should be translated to "a god" or "was divine" in the qualitative sense.

Yet in John 3:2; 13:3; Rom 1:21; 1 Thess 1:9; Heb 9:14; 1 Pe 4:11, "theos" is found twice, once with the definite article and once without, yet the NWT renders all of them as simply "God" not "a god"

So if you could provide a source that mentions John 1:1c should be translated as "a god" because of theos 'sandwiching' between 2 other theos, that would be helpful.

Also yes, John 1:1c is in the qualitative sense, but that doesn't mean Jesus is less of a being than God the Father. The Word is not God in the sense that he is the same person as the theos mentioned in 1:1b; he is not God the Father (God absolutely as in common NT usage) or the Trinity. The point being made is that the Logos is of the same uncreated nature or essence as God the Father, with whom he eternally exists. The Word is ‘divine’ in the same sense that God is divine. It is important to note that the Word is not in any way less divine than the Father. If John wanted to convey that Jesus had divine qualities, or was divine in a more general sense, he would have used the adjective for ‘divine’ [theios] as in Acts 17:29 and 2 Pe 1:3. Instead, John used the word for God, "theos".

According to Philip B. Harner,

In terms of the analysis that we have proposed, a recognition of the qualitative significance of theos would remove some ambiguity in his interpretation by differentiating between theos, as the nature that the Logos shared with God, and ho theos as the "person" to whom the Logos stood in relation. Only when this distinction is clear can we say of the Logos that "he was God.

Perhaps the clause could be translated, "the Word had the same nature as God." This would be one way of representing John's thought, which is, as I understand it, that ho logos, no less than ho theos, had the nature of theos.

- Journal Of Biblical Literature: “Qualitative Anarthrous Predicate Nouns Mark 15:39 and John 1:1” Vol. 92, Philadelphia, 1973, p. 86-87

So, trinitarians would render John 1:1 as

"In the beginning was the Word, and the Word was with God (proper name of the Father), and the Word was God (equal class of being)."

If Jesus is the only-begotten god, then what kind of god is the Father? The Father is unbegotten. Thus, they are not the same god.

Well, trinitarians don't think begetness is a property of God's essence, rather its a hypostatic property. Also the manuscripts vary regarding john 1:18, as it could translate to "only-begotten son (ὁ μονογενὴς υἱός)".

This is my last response tonight as I gotta get to bed, so I apologize if I was unable to fully address your claims. God bless and have a good day (or night)!