I believe all or nearly all commentators propose that Paul is speaking of himself in 2 Cor 12:1-7. Because he is speaking of surpassingly great revelations he received, he is using the 3rd person for himself out of humility. If you look at the context, Paul is talking about his amazing life and his accomplishments through all of chapter eleven, not to boast, but so as to show how the false apostles are deceiving the Corinthians. He continues talking about himself in 12:1-7. This use of the third person to demur about one’s accomplishments was common back then and it is even used today, although rarely, by people trying to express humility. Actually, today the first person plural is also used by individuals to talk about themselves in a humble way.
About the “third heaven” some think this means that Paul believed that there was more than one level of heaven. This is quite unlikely. To the Greek mindset there were two “heavens.” The first heaven was the sky. We would think of it as the region of the earth’s atmosphere. Some Greeks would make the first heaven include the volume between the earth and the moon. They called the first heaven the sublunary world. The second heaven, to the Greeks, was the universe beyond the sky or beyond the moon. To them, this would reach out to what they conceived of as the crystal sphere which circled the earth. The stars were embedded in this crystal sphere as far as Greek astronomers believed. To Paul, the third “heaven” would be what we typically call heaven. In other words, the first heaven is the sky, the second heaven is the rest of the physical universe and the third heaven is the spiritual abode of God. Therefore, Paul, like John in Revelation, had a heavenly vision. I cannot prove this is what he is talking about, but given what we know of the cosmology of the Greeks, this is the likely meaning of the “third heaven” that Paul is talking about.