In The Tempest, what are the differences between Prospero's and Shakespeare's plays?

I have had to edit your question because you asked two
questions. Please remember that you are not allowed to ask multiple
questions.

If I understand your question correctly, you
want me to comment on the relationship between Prospero and Shakespeare and the fact
that in this play we have several plays-within-a-play. This of course is not something
that is restricted to this play alone. In Hamlet plays-within-a-play are a central part
of the plot, as "The Mousetrap" is intended to provide proof of the guilt of Claudius.
Certainly what it does seem to do is present Prospero as the director of the action on
the island.

Much has been written of how Prospero
represents power in the play. He is on the stage longer than any other character and he
is shown to control the fate of all characters on the island. Nothing happens without
him willing it or being aware of it, and a central issue to consider is if he uses his
powers with wisdom or in a selfish fashion. Plays have varied in their depiction of
Prospero as a magnanimous ruler or a sadistic oppressive coloniser, and clearly there is
evidence for both of these options. However, the masques that are featured as part of
the action in this play rather seem to strengthen the sense of power that Prospero
holds. There seem to be many comparisons that we can make between Prospero and
Shakespeare: both direct the action and are in control of their characters, having their
destiny in their hands; both use a variety of different forms of "magic" in their dramas
and both participate in their own dramas (let us remember that Shakespeare himself
acted).