see
ncregister.com/blog/darmstrong/was-the-apostle-paul-a-priest
This quotes passages from the Bible showing that Paul definitely was a priest.
(It actually would be hard for me to believe otherwise now that this question has come up, in view of many of the things he did, shown in his own epistles.)
Yes. It is Catholic Doctrine that Jesus Christ established the Priesthood when He established the Eucharist saying:
Matthew 26:26 And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body.
27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;
St. Paul also received this Teaching from Christ:
1 Corinthians 11:23 For I have received of the Lord that which also I delivered unto you, that the Lord Jesus the same night in which he was betrayed took bread:
24 And when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me.
25 After the same manner also he took the cup, when he had supped, saying, this cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me.
And he admits that he confects the Eucharist when he says:
1 Corinthians 10:16 The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?