1. Paul praised them for keeping the ordinances he had delivered (v. 2).
2. A headcovering or the lack thereof (vs. 4-5) is a public rather than private issue.
3. Paul regulates both men (v. 4) and women (v. 5) praying and prophesying and gives no indication that the acts of the men and the women are in distinct settings. We know that men prayed and prophesied in the assembly.
4. Paul expresses his concerns to a plural "you", which is the object of his letter -- the church at Corinth (1:2). There is no contextual reason to suppose the "you" of 11:2-3, et al. is a different "you" than that of 11:17-18, et al.
5. The presence of the angels in reference to a headcovering (v. 10) most likely refers to worship; otherwise they are present at times when no headcovering would be expected -- sleeping, washing hair, etc.
6. Prophecy is a speaking gift whose end is someone listening, so therefore not a private gift. The main purpose of prophecy is the edification of the church (Cf. 1 Corinthians 14:3-5,31).
7. The “have no such custom” argument in this context (v. 16) refers to customs in “the churches of God.”