I agree with you for the most part but wanted to add this for your thoughts on why I personally don't think we can call the communication between ones individual spirit to the Spirit of God a "prayer language" or tongue.
I believe the scripture that you are talking about is Romans 8:28 "In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express."
Key words in this vs are groans and words cannot express. Since the text tells us that the spirit "groans" I don't classify it as a tongue. Tongues can be interpreted but the groan described cannot be expressed through words which to me can't be interpreted so it is not a tongue.
As you pointed out tongues are to be interpreted for the edification of the entire body. Groans are spiritual intercession, unctioned by the Spirit of God during weakness. Again since its a groan and not words, then can we call it a language? Although there are several definitions of language. One of them is "a body of words and the system of it's use."
I do believe that speaking in tongues is a gift from God and should be used even today under the will of God. I also believe that it is personal for each individual that God gifts it to since each of us are individuals and are used according to our individuality. Im just not sure that I believe it to be a personal language since according to scripture, tongues should be interpreted. Someone should be able to interpret the tongue each one speaks which really doesn't make it our own personal prayer language. IMO.
Amen. I do wholeheartedly believe that.
Mrs. Richard posting on my iPad using CF