Coming a bit late to the party, but some thoughts anyway...
Some sincere questions.....
1. According to the words in the New Testament, what exactly IS this? Do we have an exact definition, description so that we can determine what is and is not "speaking in tongues?" How specifically are we told to recognize what it is and is not? Is there ONE speaking in tongues or endless varieties of this? Is "speaking in tongues" today thought to be the same or different from that mentioned in the Bible?
In Acts chapter 2 we see the Holy Spirit descending and people speaking with other tongues (2:4). We can see that the tongues were known human languages as people from all around heard their own language (2:6-11). The gift of tongues served a specific purpose here.
Today, aside from having a gift of discernment (which is perhaps a topic for another thread) I'm not sure there is some way of determining whether someone is speaking in tongues or uttering gibberish. Anyone can whisper
shundai, kushanda and sound like they are speaking in tongues. On the other hand if someone present recognises the language and can verify its meaning that's a good sign that the tongues are genuine.
Years ago I heard a guy I knew praying in tongues, and I remember hearing one specific word repeatedly (it's not the only time that happened, I picked out the term for "God" in another language when hearing a native speaker of it praying as it occurred many times). Recently I was reading a Hebrew dictionary and suddenly realised that one of the words I was looking at matched the sound this guy had been making when praying. I don't think he knew Hebrew (I could be wrong), but on knowing him and seeing that (admittedly not court-proof evidence) I was satisfied that he was praying in Hebrew.
There's some disagreement over the meaning of 1Co 13:1 where Paul writes of speaking in the tongues of men and angels. Some say it means "I speak in the tongues of men and angels but if I have no love it means nothing" while others say it means "If I speak in the tongues of men, and even if I speak in the tongues of angels, it would be worthless if I have no love". The latter is critically different because it's equivalent to "even if I could leap the tallest buildings it would be for nothing" as opposed to "I can leap tall buildings but..."
2. People (sincerely, I believe) claim to "speak in tongues." I've met several. How do we know that what they are doing IS exactly what people where doing 2000 years ago which they called "speaking in tongues?" I'm NOT asking if they are DOING something (they are, IMO).... I'm NOT asking if it's a spiritually moving thing for them (I'm sure it is)..... I'm NOT asking if they are sincere (I'm sure they are), I'm asking how do we KNOW - from the verbatim words found in the NT - that what they are doing IS specifically "speaking in tongues" as the NT speaks of it?
Short of recognising the language I don't think there is a foolproof way we can verify that the sounds they are making are useful, any more than someone describing their dream or vision can be exhaustively tested. The difference with a dream or vision is that it can be considered for meaning and any meaning considered can be tested against the known word of God. If someone is uttering a load of sounds that make no sense it's all but impossible to know for sure whether they are speaking in tongues by the power of the Holy Spirit, speaking in tongues by the power of demons, speaking a language they naturally know, or making up a load of gibberish.
3. When I was a teen, a good friend of mine had a mother who was a self-proclaimed and self-ordained Apostle, Prophet, Bishop, Faith Healer and Pastor. She also claimed she had numerous gifts - including speaking in tongues and interpretation thereof. (BTW, I was still on her email list as of a year or so ago.... I got regular updates on revelations she got directly from God; always quite interesting: another matter for another thread). I asked her daughter these two questions and she had no reply, but when she asked me if I speak in tongues, I told her I'm not sure I have any way to know. She told me to say a sentence. "Praise precious Jesus Prince of Peace." Say it with my heart and my mouth. Fast. Faster. Faster still! And if I did - with all my heart..... with great speed.... the Holy Spirit would fall upon me and would give me the Gift of Tongues and I'd just KNOW that I have it. I tried it. It was very hard to do without stumbling - and eventually, that's what I did. Was I speaking in tongues? How do I know? How do you know?
Honestly, this kind of thing makes it easier for people to ridicule speaking in tongues. The Holy Spirit isn't an option in a cosmic vending machine where you press the right buttons, pull the lever, and you get the gift of tongues. Paul is clear in 1Co 12:30 that not everybody will speak in tongues. There are many gifts that are given as the Spirit decides (1Co 12:4).
4. What is it's purpose in the church? According to the Bible and/or proponents?
Aside from being misused in some quarters to prove a higher degree of spirituality (I've read at least one author who seems to believe that unless you speak in tongues you don't have the Holy Spirit at all, and if you don't speak in tongues you can't possibly have any other gifts. Maybe Paul got it wrong...), it does have purposes.
I've come across a few cases (that posted on a forum are little more than hearsay, but I trust the people enough to believe their stories are true) where people have prayed for someone in English only for that person to "know they were OK" because "they spoke such beautiful (language)". The person concerned prayed in English because they didn't speak the other person's language, but the other person heard their own language. I was personally once in a situation where someone prayed and I heard gibberish but the person next to me (who I trust pretty much without limit) heard English.
Looking purely at Biblical expressions of its purpose, they may be used in public in church but they must be interpreted (1Co 14:27) and if no interpretation is forthcoming the person should be silent in church (1Co 14:28). Aside from the situation where no interpretation is forthcoming, Paul also writes that speaking in tongues should not be forbidden (1Co 14:39).
The person speaking in tongues edifies himself (1Co 14:4) although it seems reasonable to assume that when spoken out and duly interpreted it can edify the church.
In 1Co 14:22 Paul writes that tongues are a sign to unbelievers. For a sign to be useful to unbelievers the unbelievers in question would have to hear a language they understood - a roomful of people mumbling a load of unintelligible gibberish wouldn't be much of a sign to anyone. So that further confirms the validity of their use when speaking to those who do not believe, if the tongues in question are human languages understood by the listener.
Romans 8:26 refers to "groanings which cannot be uttered". Some say this is a reference to other tongues, although personally I find it hard to see how something with cannot be uttered can refer to speaking another language.
One belief I consider to be damaging is the notion that tongues are the only valid evidence of the Holy Spirit. In Acts 2 we see the disciples speaking in other languages as they received the Spirit, and likewise in Acts 19:6 Paul laid hands on people and they received the Holy Spirit and spoke in tongues and prophesied. But to insist that because God worked in that particular way then means he can only work in that way now seems excessively restrictive, especially in the light of what Paul wrote in 1Co 12:29-30 that basically says not everybody has every gift. So on that basis I'd say that tongues may be a valid expression of the presence of the Holy Spirit but a lack of tongues doesn't mean a lack of the Spirit. Jesus said we would know people by their fruits, not by their gifts.