In what manner and under what authority does Albany reclaim power that Edmund may have? ( King Lear, V, iii)Also, How is the power of the realm...

Albany is son-in-law to the King and husband to Goneril,
and as such, holds much power.  In the fight against the French armies, he holds
authority and commands the troops.  Edmund begins the play as a usurper (He deceives his
half-brother Edgar, in an attempt to gain their father's lands and title.), and
continues his villainous and deceitful actions all through the play.  Act V, Scene iii
is no exception.

Edmund has commanded the soldiers to
imprison Lear and Cordelia, but upon his arrival, Albany challenges Edmund's authority
to issue such orders.  Albany insists, rightly so, that he has no such authority,
calling Edmund a "Half-blooded fellow," and saying,

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I hold you but as a subject of this
war,

Not as a
brother.

Meaning that Albany
does not see Edmund as an equal.  He commands that Edmund be arrested on the charge of
"capital treason."

As for the end of the play:  King Lear
is dead.  Albany is the next in line to the throne and he begins by making amends with
the true and loyal subjects Kent and Edgar, now Duke of  Gloucester.  This ending could
be considered dis-satisfactory since Albany has spent the majority of the play on "team
villains," yet Shakespeare, in only a few moments, wants the audience to accept him as a
sort of hero.  Does this work?  That's up to each individual audience
member.

There is certainly much more to comment on about
the "satisfaction" of the ending, for this has been a topic of debate for centuries,
even sparking a rewrite of the play in the 19th century in which Cordelia does not die,
but, instead, marries Edgar at the end of the play.  In this version, they will rule the
kingdom.

There is also much discussion, and has been
through the centuries about the themes of the play.  Power/Authority and who has it is
certainly a major issue in the play.  So are the themes of patriarchy, madness, sight
(figurative and literal), and more.  Again, you should arrive at the answer to the
question of theme based upon your response to the events of the play, for there is no
one "right" answer.