I would also try to keep a balance in some of this. Christ does intercede for us and on our behalf before the Father.
Here is a small portion of Calvin...
(Heb 7:24) But this man, because he continueth ever, hath an unchangeable priesthood.
(Heb 7:25) Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
(Heb 7:26) For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens;
(Heb 7:27) Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself.
(Heb 7:28) For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore.
Seeing he ever liveth, etc. What sort of pledge and how great is this of love towards us! Christ liveth for us, not for himself! That he was received into a blessed immortality to reign in heaven, this has taken place, as the Apostle declares, for our sake. Then the life, and the kingdom, and the glory of Christ are all destined for our salvation as to their object; nor has Christ any thing, which may not be applied to our benefit; for he has been given to us by the Father once for all on this condition, that all his should be ours. He at the same time teaches us by what Christ is doing, that he is performing his office as a priest; for it belongs to a priest to intercede for the people, that they may obtain favor with God. This is what Christ is ever doing, for it was for this purpose that he rose again from the dead. Then of right, for his continual intercession, he claims for himself the office of the priesthood.
seeing he ever liveth to make intercession for them; Christ ever lives as God, he is the living God; and though he died as man, he is risen from the dead, and will not die again, but live for evermore; and he lives as Mediator and Redeemer, and particularly as a priest; one branch of whose office it is to intercede for his people: this he does now in heaven; not by vocal prayer and supplication, at least not as in the days of his flesh; or as if he was supplicating an angry Judge; nor as controverting, or litigating, a point the court of heaven; but by the appearance of his person for them; by the presentation of his sacrifice, blood, and righteousness; by declaring his will, that such and such blessings be bestowed on such and such persons; and by recommending the prayers of his people, and removing the charges and accusations of Satan: the things he intercedes for are, the conversion of his that are in a state of nature; the consolation of distressed ones; fresh discoveries of pardoning grace to fallen believers; renewed strength to oppose sin, exercise grace, discharge duty, and bear up under temptations, and deliverance out of them; perseverance in faith and holiness, and eternal glorification; and he intercedes for these things; not for all the world, but for all the elect, even though transgressors; and he is very fit for this work, as the following verse shows; he is the one and only Mediator; and he is a very prevalent intercessor, he always succeeds; and he does this work readily, willingly, cheerfully, and freely; and all this proves him to be able to save; for though the impetration of salvation is by his death, the application of it is owing to his interceding life; had he died and not lived again, he could not have saved to the uttermost; his life is the security of his people's, and he lives for them, and as their representative; the blessed, effects of which they constantly enjoy.
Does not Christ and the Spirit intercede for us and on our behalf? Yes. I just don't remember hearing anyone say that Christ loved us and caused the Father to love us if that is what you are speaking about. And that is why I made my first statement the way I did.
5. There is a change in that covenant of which the priesthood was a security and the priest a surety; that is, a change in the dispensation of that covenant. The gospel dispensation is more full, free, perspicuous, spiritual, and efficacious, than that of the law. Christ is in this gospel covenant a surety for us to God and for God to us, to see that the articles be performed on both parts He, as surety, has united the divine and human nature together in his own person, and therein given assurance of reconciliation; and he has, as surety, united God and man together in the bond of the everlasting covenant. He pleads with men to keep their covenant with god, and he pleads with God that he will fulfil his promises to men, which he is always ready to do in a way suitable to his majesty and glory, that is, through a Mediator.