Historically, no. Macbeth was succeeded by his stepson Lulach, who only reigned a short time. Shakespeare cut Lulach out as an unnecessary character (although we do hear that Lady Macbeth has "given suck" which must refer to him.) and had Malcolm succeed Macbeth. Historically inaccurate but dramatically more satisfying.
At the end of Shakespeare's play Macbeth; Malcolm, son of Duncan is proclaimed to be King of Scots. (In actual history, Macbeth was succeeded by his son Lulach; who was then was assassinated and deposed by Malcolm)
The English army, led by Malcolm and Siward, invades Scotland at the end of Macbeth to overthrow Macbeth's tyrannical rule and restore Malcolm as the rightful king.
At the end of Macbeth, the nation that assists Malcolm and the Thanes in invading Scotland is England. King Edward lends military support to Malcolm in his quest to overthrow Macbeth and reclaim the Scottish throne.
"This dead butcher and his fiendlike queen" Nice, eh.
Malcolm resolves to lead an army against Macbeth and reclaim the throne of Scotland. He plans to gather troops and overthrow Macbeth's tyrannical rule.
At the beginning of the play, Macbeth didn't have any enemies. By the end he had lots, including Malcolm, Donalbain, Fleance and especially Macduff.
Macbeth does not believe that Malcolm cannot harm himself. He is quite prepared to believe that Malcolm might harm Malcolm, which is what "harm himself" means. Macbeth does believe that Malcolm cannot harm him (i.e. Macbeth) because Malcolm's mother was apparently a woman and the witches said that none of woman born could harm Macbeth.
In the end it is Malcolm who finally slays Macbeth. No! Rubbish! Malcolm is a useless soldier and couldn't kill Macbeth if Macbeth were tied hand and foot. It was Macduff, the man "not of woman born", who kills Macbeth.
In the play Macbeth, Malcolm portrays himself as a potential sinful tyrant in order to to test Macbeth. Malcolm wanted to see just how loyal Macbeth would be.
In Macbeth? King Duncan names his son Malcolm The Prince of Cumberland who is the heir apparent. After his murder, Malcolm flees so Macbeth is named to be King but later on in the play Malcolm, Duncan's son, becomes king.
In the play Macbeth, Malcolm joins forces with the English commanded by Siward and a number of disgruntled Scotsmen including Macduff.
Well, just about everyone really: Ross, Lennox, Angus, Caithness, and a lot of Scottish lords. One person is conspicuous by his absence--Malcolm's brother Donalbain.