So do you find the term Mormon derogatory?
Not derogatory, just misdirected. Jesus Christ heads the church, not Mormon, a Book of mormon prophet, circa early 5th century CE, named for him as he was its editor from a much larger group of records.
Savior and redeemer of what and from what?
Savior of man from perpetual death following mortality by resurrection to life everlasting in perfect bodies, and redeemed from the influence of evil forever more, conditional on keeping the commandments of God.
Jesus is begotten - but eternally begotten. And they would also say that Jesus is not mortal.
To beget is to be born in the flesh. We are born but once, and birth does not extend beyond that moment, so no one is beget eternally, not even Christ. Christ is no longer mortal, having died and resurrected, the first of all to do so, and the promise to all men, women, and children who die - all of us.
Is this the same as the Holy Spirit?
Yes, the same.
Three persons in One Godhead?
Yes, as long as it is understood by this that we mean three separate, distinct beings who comprise the Godhead, not one being with aliases, as some believe.
similarities
That Jesus is the Christ, the living Son of a living God, the Father.
However, there is much with which we disagree. For example, we do not believe we bare the stain of Adam and Eve for their transgressions, but only for our own. To believe that we bear Adam's stain is a denial of the Atonement, that Jesus overcame death, but also our pain and suffering, disappointments, mourning for losses, suffering by the actions of others who abuse us, our failures of mortality, virtually everything that happens in our mortal lives that deter us and delay our progression. We are spared the ongoing misery of death, itself, to rise in the resurrection as perfect beings, ready to move on in that progression.
Not a similarity, in fact, it may be somewhat unique among Christians is that we believe the potential of our progression is eternal; thaat we, by our obedience in this life, can earn the right to become gods and goddesses ourselves, to be not only in the image of God, by to be like him.
We may also be somewhat unique in the firm belief that we have a Mother in Heaven, whom we should also revere.