Thank you very much. I included my corrections in brackets (nearly always).

1)I can't understand one of your corrections: he wishes the portrait would grow old in his place (why is "grew old in his place" wrong?)
2)Beauty has got a divine right of sovereignty and (since) it is the only mean to stop time.
3) According to Lord Henry, the time (time) is jealous of beauty.
Henry implores Dorian to enjoy youth while he can, because during the aging process (when he grows old) he would (will) become hollow-cheeked and sallow.
4) Owen describes the death of his friend, his skin which is falling down (falling off his face) and the bloody gargling in his lung ( and his blood gargling in his lungs).
5) Dorian remains fascinated by the picture as well as by his own youth and beauty.
6) He wishes to stay young forever instead the picture grew old Better: he wishes he could stay young forever whereas the picture grew old in his place.
7)Dorian wants to free himself from (of) the portrait.The wishes of eternal beauty and youth : the desire for eternal beauty and youth could be connected to Goethe’s Faust.
8) He tells Dorian that beauty won’t last forever and that he, therefore, should enjoy his youth while he can.
In contrast, the aging process makes people sallow.

1. You need "would" because it's a wish, not a fact.

2. I don't understand this sentence.

3. time (not "the time")
during the aging process, he will become...

4. Owen describes the death of his friend, whose skin is falling off his face, and whose blood is gurgling in his lungs.

5. comma needed

6. Yes, use the "better" phrasing. Where will you put the comma?

7. from (not of); space after period; why is there a colon? Faust - in italics

8. OK