For example, if you were falling, facing upwards, and you Disapparated, would you continue to move backwards really fast once you got there? If so, could you change your momentum by Apparating to a different orientation? And if not, doesn't that, like, break the laws of physics and stuff?
This question is difficult to answer because those who Apparate tend to begin fairly steadily. It requires concentration to Apparate and generally helps to turn on the spot while doing so, which means that you need to not be having too much linear momentum in order to do so properly.
That said, consider the (unfortunately rather gruesome) example of when Harry and Dobby Disapparate from Malfoy Manor. This is when Bellatrix's knife Disapparates along with them and ends up piercing Dobby in the chest.
Hoisting the groaning goblin, who still clung to the sword, over one shoulder, Harry seized Dobby’s hand and spun on the spot to Disapparate. As he turned into darkness he caught one last view of the drawing room: of the pale, frozen figures of Narcissa and Draco, of the streak of red that was Ron’s hair, and a blur of flying silver, as Bellatrix’s knife flew across the room at the place where he was vanishing . . . Bill and Fleur’s . . . Shell Cottage . . . Bill and Fleur’s . . . He had disappeared into the unknown; all he could do was repeat the name of the destination and hope that it would suffice to take him there. The pain in his forehead pierced him, and the weight of the goblin bore down upon him; he could feel the blade of Gryffindor’s sword bumping against his back; Dobby’s hand jerked in his; he wondered whether the elf was trying to take charge, to pull them in the right direction, and tried, by squeezing the fingers, to indicate that that was fine with him. . . .
I'm making a small assumption here, which I believe is the correct one judging by Rowling's tendency to giving a misinterpreted piece of information whose true significance is revealed afterwards, and the assumption is that the moment when "Dobby's hand jerked in his" was the moment when the knife fully plunged into his chest; the impact of the knife thrusting into his chest had made him jerk in pain. When that happened, however, Harry and Dobby were already in the process of Apparating, in the period of darkness that usually accompanies an act of Apparition when one has left the point of origin but has not yet arrived at the destination.
This would imply that at the moment when they had started Apparating, the knife had not yet plunged itself into Dobby's chest; its point may have just reached him, which would explain why the knife Apparated with them as it would have needed to be in contact with one of the parties Apparating to do so, but it had not yet fully planted itself into Dobby's chest until that jerk.
Afterwards we learn that the knife has buried itself deep enough to kill Dobby and, in particular, to stay in his chest while he was standing upright. If objects were to lose momentum during the course of Apparition, the knife would have simply stayed with its point against Dobby's chest and would have merely fallen to the ground once they'd arrived. Instead, the momentum it had gained from Bellatrix's throw continued to propel it forward during the course of Apparition.
So the answer, I believe, is yes; Apparating objects keep their momentum. Poor Dobby.
Deductive speculation: yes
What about in Harry Potter and The Deathly Hallows, Chapter 13 / 14?
(end of Chapter 13)
'LET'S GO!' Harry yelled. He seized Hermione by the hand and Ron by the arm and turned on the spot. Darkness engulfed them....Hermione's hand seemed to be slipping out of his grip....
Harry opened his eyes....he was lying on what seemed to be leaves and twigs...Harry started crawling towards him [Ron]...he met Hermione.
later in the scene, Hermione speaking:
Yaxley caught hold of me, and I couldn't get rid of him, he was too strong...I managed to shake him off and brought us here
This is speculation based on this scene but we may be seeing a couple of things here that show us that you can alter your physical orientation (deliberately or not) via Apparation. Harry is holding both Ron and Hermione and, while standing, he pivots, which has some element of momentum to it. In the course of their journey, Hermione is grabbed by Yaxley and this alters everyone's orientation. They become, not only separated, but Harry, who had pivoted and was likely using the weight of the other two for his balance and positioning, lost hold of them both. He lands separated as well as prone (when he had been standing). There is no mention of Yaxley explicitly interfering with Harry physically so we can assume that his initial pivot was based on his point of reference with Ron and Hermione. When they became separated, his pivot had become overcompensated for just him spinning and he fell through space and time and fell on his back away from the other two.
It is forbidden to break the law of physics. Even in Harry Potter universe.
When somebody uses magic he get tired because he is wasting his own energy; not a meaningless or spiritual kind of energy, I am talking about ATP and stuff. Energy is conserved.
When somebody dies in Harry Potter universe is absolutely impossible to get back to life. Why? Death is the thermodynamic equilibrium, the maximum entropy a lifeform can achieve. It is impossible to go back to life because of the Second law of thermodynamics.
Apparition does not break any law of physics. You just must conserve your momentum. If we read carefuly at the books, we'll see that people who apparate running is still running after that. Momentum is conserved.
Henceforth, with all the magic and all the fantasy that you can imagine. Harry Potter universe respect every single law of physics.
P.S. If there is anything that you can not explain with physics in Rowling's world. It is probably because of Quantum Mechanics.