Jesus is in Heaven, yes. To say “we are sacrificing him for our sins” is a pretty tricky phrase. I would say, rather, that Jesus has already sacrificed himself for us, and that we are participating in that once-for-all sacrifice by re-presenting it, under the forms/appearances of bread and wine. Look at it this way: Jesus offered himself in a bloody manner on the cross, but he also offered himself in an unbloody manner the night before, to his disciples, under the appearances of bread and wine. So we too, today, are offering Jesus to the Father under the appearances of bread and wine. It is not a NEW sacrifice, or ANOTHER sacrifice, but the same sacrifice made present again.
As for “he is bleeding in heaven”, that is again a rather tricky phrase. Perhaps the priest was alluding to the image that the apostle John saw, recorded in the book of Revelation: he saw, in Heaven, an altar, and on the altar a lamb stood, looking as though it had been slain, but the lamb was very much alive. That lamb is Jesus, the “lamb of God” (see the first chapter of the John’s Gospel). He appears as a slain-but-living lamb, because he was crucified but resurrected, still bearing the signs of his death: the wounds in his side, hands, and feet. I would not say “Jesus is bleeding”, because of the way it sounds, and the images it might induce; rather, I would say that the Eucharist shows the death that Jesus suffered for us, but in the unbloody signs of (broken) bread and (poured out) wine.
(By the way, this distinction between “bloody” and “unbloody” is one that has been used for centuries to describe the difference in manner and appearance between the Crucifixion and the Eucharist.)
There is a part of the Mass where the priest takes the consecrated Host and breaks it into smaller pieces – this is called the Fraction Rite, because he is fracturing (breaking) the Host. This act represents several things, one of which is the injuries suffered in Christ’s body during his Passion.
At this point, the priest takes a small portion of the Host and places it into the Chalice; he mingles the consecrated bread (which visually represents the Body) with the consecration wine (which visually represents the Blood). This represents the resurrection, the
reunion of Christ’s body and blood in his resurrected, glorified self. This is because the bread and the wine are consecrated separately, representing the
separation of his blood from his body – his death. They are reunited in the Chalice (hidden from view, as was the resurrection).
The linen on the altar that is used during the Liturgy of the Eucharist is said to represent the burial cloth, yes. It is, in fact, called a “corporal”. In the older form of the Roman Rite (i.e. what was celebrated before Vatican II) the consecrated Host would be placed directly
onto the corporal; nowadays the Host stays on a plate called a paten. But that was why the cloth was called a “
corporal” – because upon it rested the Body (
corpus) of Christ.
That’s a rather blunt way of describing it; perhaps I just shy away from bluntness when talking about the Eucharist…
God is present in the Eucharist, so yes, insofar as the Eucharist is “lying there” on the “burial cloth”, “waiting” for us to “consume” it, God is too. But that language is too strong on the physical / local / material senses of presence. I would say, rather, that God is present on the altar in the Eucharist, inviting us to come and receive Him.
Another blunt saying.

We offer God the only sacrifice that can truly be worthy of God: Himself. He knows! He’s already made the sacrifice! We’re there uniting ourselves to it, so that we are partakers not only in receiving the sacrifice as food, but also as partakers in offering ourselves with Jesus.