There are WAY too many questions here, too many caveats and differing circumstances, and on top of that, is pretty opinion-based and seems to be more about plot generation than world-building. But hey, I'll take a stab...
What if a guilty person made a clone of themselves, and implanted
their memories into the clone?
Would the clone also need to be punished?
Has the original already served their sentence?
What if the original died/didn’t die after implanting the memories?
They can't be both alive and dead. I guess this is actually two questions and not one if it refers to two different states of being.
Are they using this to get out of their sentence?
Will the original be serving their sentence?
The questions I am posing, that you'll see have a pattern, have something to do with the legal concept of double jeopardy--that is, that you can't be tried for the same crime twice, or punished for it twice. If the clone is a continuation of original criminal X and they use cloning and death to get out of punishment, if the clone is legally still them, they would finish out the sentence. If, however, the original lives on, they can finish out their own sentence, while the clone walks free. You can't punish one person twice for the same crime.
This only works if the lawyer can prove that the clone is the same person. If, because they are a baby, and not the same age as the person known as Criminal X, despite all the memories and identical DNA it might be possible to prove that they are not the same person.
As a side note, I have no idea how you'd make a baby serve hard time.
ALL THE QUESTIONS CONCERNING MEMORIES AND NON-CLONES OR A CLONE THAT POSSIBLY HAS THEIR OWN MEMORIES OR OTHERS
It seriously does not matter. Legally not the same person, memories or not. You'd have to prove that they were the same person, which would be much easier to prove legally if they were also clones and/or had no other memories/personality. But for the sake of argument, apply all the logic from the other answers above as well.
Is the child a biological descendant of the criminal?
You tell me. You have different conditions applied to the different questions.
Were the memories implanted in the child at birth?
Again, you have different circumstances applied in each instance.
Were any other person’s memories implanted when the criminal’s
No idea. This is your story, not mine. This site is here to answer questions concerning world building, not be a way to generate plot points.
What's the difference, you might ask? The questions would be more focused on a single point, and more about the world/legal system rather than people's opinion. "Given a world with a judicial system evolved from the current British system, 200 years in the future, would the clone of a criminal who deposited his entire mind in his clone be considered responsible for his crimes? How might a legal system like this one handle such a thing? Would the clone have to finish out the criminal's sentence if the criminal died right after the process? And if the criminal did live, would the clone have to serve for the crimes with him? Clone starts as a baby with all the memories FYI." OR "Two hundred years into the future, memory transfer and cloning is possible. If all of a criminal's memories can be transferred to their blank slate clone, would that clone be responsible for the criminal's crimes legally, given a future legal system borne from the United States of America?"
Did the criminal die shortly after the memories were implanted?
Again, how am I supposed to answer that question? Wait, I've got it! They are alive/dead. Schrodinger's Criminal. :)
You're new, so visit this meta on asking questions. YOu'll get the hang of it!