I am a small student of greek. I was curious about what you say above. You might need to explain more. I looked up the passage in Matthew 2:1, Acts 2:8 and several other similar contexts. All the words went back to the same root of ginomai. I am not sure I am making any serious point here because languages do not have a word for word parallel and there is room for a domain of meanings. Both meanings you post above could be included as within the domain of the word ginomai, so I do not have any objection to your conclusions above, I merely do not understand the process by which you got there. Can you point to the specific text that does not have the root ginomai?
How would you read Acts 2:4 "and began to speak with other tongues?"
How would you read the 2nd part of Acts 2:6
"because each one of them was hearing them speak in his own language."
I would definitely agree here and feel this is the major point of true biblical tongues that should be stressed. 1 Corinthians 14:22 is definitional. This specific statement defines what tongues was about.
Paul, in the preceeding verse quote a passage from Isaiah 28:11 as proof of his idea that tongues is a sign gift to unbelievers. The context of Isaiah 28:11 is the Assyrian invasion of Judah. I am open to discussion on the relationship between the two passages (1 Corinthians and ISaiah 28), but my opinion is that Paul is using Isaiah 28:11 to point to the fact that Israel, the nation, has come under the curses of Deuteronomy 28:15ff to Deuteronomy 28:46. This is a long story--and I am not going to write much on this, but notice what Moses says in Deuteronomy 28:46... "They shall be a sign and a wonder against you and your offspring forever." Isaiah takes up this theme in his discussion in Isaiah 28 in the context of the "Day of the Lord." (see Isaiah 28:5 "In that day the LORD of hosts ... also 27:1; 26:1; 25:9). In Isaiah 28, when the Israelites heard foreign languages, it was to be seen as a sign that Israel was under the curses of Deuteronomy 28.
So then, in the Apostolic Church, (1) tongues was for a sign of Israel's judgement, and it was (2) also related to the "day of the Lord." (However, he careful with the concept of the Day of the Lord because 2 Thessalonians 2:2 makes it clear that we are not yet in the "Day of the Lord." This gets into the "now and then" concept of Christian eschatology. That is another long issue I am not going to write on here and now. Therer is reason # (3) for tongues I will mention below.
Are you sure that the unbelievers could not understand the language being spoken? In Acts 2:11 the text says they heard them "in their own tongue." Then after hearing the words, they mocked.
Here is reason #3 for tongues.
The concept of signs and wonders again comes up in Acts 2:43. The signs are there limited to the apostles. Is it not fascenating that Luke mentions the concept of Apostolic signs in the narrative portion of Acts and Paul mentions signs in his explaination of tongues in 1 Corintians? Apostolic signs were necessary because the Apostles were the authoritative eyewitnesses that give to the church revelation (the NT). Just as OT prophets gave signs of their authority (all the way back to Moses), so also NT apostles and prophets gave signs. Paul says in 2 Cor 12:12 "The signs of a true apostle were performed amount you with all perseverance, by signs and wonders and miracles." So then, there is another purpose for signs, to validate a revelation. Of course, being to the reformed side, and believing in sola scriptura, I reject modern day apostles, and thus modern day revelation. So then, I also reject sign gifts related to apostleship (including tongues). I think there are reasons no books of been added to the scriptures for 1900 years. There are no more apostles, and no apostolic successors. The completed scriptures, the bible is enough. The need for signs ceased with the need for apostles and prophets. The need for apostles and prophets ended with the completion of the scriptures and the bibles completed authority.