In regards to Baptism of the Holy Spirit:
1 Corinthians 12:13
13 For by one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink into one Spirit.
His main point? All believers have been baptized by the Spirit.
What does it do? It makes us part of the body of Christ, the Church.
When did it happen? If every believer has been baptized in the Spirit, then it must happen at the moment you accept Christ and become a Christian.
Being a Christian is to be "in a covenant" relationship with God. I am not sure what else you mean by being "in covenant". Perhaps you are talking about Covenant Theology as a whole?