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In reference to the Acts passage:
The believers speaking in native tongues is a throwback to a Midrash on the Sinai event when the Law was received. The rabbinic retelling has Israel speaking in all the tongues of the world, meaning that this is a monumental act of GOD happening. The gospel is here, guided by the spirit and is intended for all peoples of the world, thereby undoing the judgement of the tower of babel.
The midrash is from Midrash Tanhuma 26c, as referenced in the book Speaking in tongues: the New Testament evidence in context.
And in respect to the Corinthians passages:
They are In respect to the spirit of GOD speaking through someone for the building up and edification of the local church and therefore not necessarily with the intention of evangelism. The Corinthians used to fake speaking in tounges because they wanted to be seen as spiritual but here Paul is putting an end to that by saying don't speak in tongues in church unless there is an interpreter.
Craig keener, a Pentecostal evangelical conservative scholar has a great commentary on this called 1 + 2 Corinthians, it's totally worth the money.