Yes, the same category as modes of communication requiring intelligible speech. Just as psalm, doctrine, tongue, revelation, and interpretation (ver. 26) are different modes of communicating the same message.Actually - he draws the distinction that prayer and song should be intelligible and spirit filled - not one or the other is to be unintelligible in worship - thus placing song and prayer in the same category.
No, "spirit" does not refer to spirit filled, but spirit inspired. The opening words of the section dealing with "spirituals" in 1 Cor. 12:1-3 made it clear that the apostle was addressing the situation where men claimed to be speaking "by the Spirit of God." And the closing section in verses 36-40 makes it apparent that the apostle is challenging these "spirituals" who claim to be speaking by the Spirit of God, insisting that the truly spiritual amongst them will recognise that the things he writes "are the commandment of the Lord."