The Covenant Before Baptism

Question Regarding Baptism

Now here is an interesting question regarding baptism and the purpose for it. First lets take a look at three different verses. Three witnesses should be enough right?

Mosiah 18:10
Now I say unto you, if this be the desire of your hearts, what have you against being baptized in the name of the Lord, as a witness before him that ye have entered into a covenant with him, that ye will serve him and keep his commandments, that he may pour out his Spirit more abundantly upon you? 

3 Nephi 7:25 Therefore, there were ordained of Nephi, men unto this ministry, that all such as should come unto them should be baptized with water, and this as a witness and a testimony before God, and unto the people, that they had repented and received a remission of their sins.

D&C 20:37 And again, by way of commandment to the church concerning the manner of baptism—All those who humble themselves before God, and desire to be baptized, and come forth with broken hearts and contrite spirits, and witness before the church that they have truly repented of all their sins, and are willing to take upon them the name of Jesus Christ, having a determination to serve him to the end [there's your covenant again as shown in the previous two verses], and truly manifest by their works that they have received of the Spirit of Christ unto the remission of their sins, shall be received by baptism into his church.

Why is it in each of these cases the covenant past tense? Why is it they had repented? Had received a remission of their sins which only comes from baptism by fire and the holy Ghost right? Isn't it the Holy ghost that purifies the blood to become clean again? Even as fire? Does baptisms really have the covenant or is the covenant something made and baptism is merely a sign (witness) that one has already entered the covenant?

Most importantly how is it they had received a remission of their sins BEFORE they had even “received the gift of the Holy Ghost by laying on of hands” and "baptism by water"?

Baptism prayer

25 Having authority given me of Jesus Christ, I baptize you in the name of the Father, and of the Son, and of the Holy Ghost. Amen. (3 Nephi 11:25)

Thats it. Nothing in the prayer that relates, a covenant, forgiveness of sins, etc...

So where did this covenant as seen in Mosiah 21 come from if it was not baptism?

31 Yea, they did mourn for their departure, for they knew not whither they had fled. Now they would have gladly joined with them, for they themselves had entered into a covenant with God to serve him and keep his commandments.
32 And now since the coming of Ammon, king Limhi had also entered into a covenant with God, and also many of his people, to serve him and keep his commandments.
33 And it came to pass that king Limhi and many of his people were desirous to be baptized; but there was none in the land that had authority from God. And Ammon declined doing this thing, considering himself an unworthy servant.
34 Therefore they did not at that time form themselves into a church, waiting upon the Spirit of the Lord. Now they were desirous to become even as Alma and his brethren, who had fled into the wilderness.
35 They were desirous to be baptized as a witness and a testimony that they were willing to serve God with all their hearts; nevertheless they did prolong the time; and an account of their baptism shall be given hereafter. (Mosiah 21:31-35)