In act 4, scene 3 , why is Malcolm not ready to express his grief in front of common public? And why does he wants to go to a lonely place?
I assume you are referring to what Malcolm says in the beginning of the scene in his first two speeches ("Let us seek out...bosoms empty." and "What I believe, I'll wail..."). Malcolm is grieving for Scotland and he suggests to Macduff that they sit and talk. Malcolm tells Macduff that he isn't completely trustful of him yet. He suggests that perhaps Macduff, who was once loved by Macbeth, is really only there in England to trick Malcolm in to returning to Scotland so that Macbeth could kill him. Macduff despairs of being able to convince Malcolm of his loyalty to Malcolm, and especially to Scotland.l Malcolm then tells Macduff that he would be a far worse king than Macbeth because his vices and sins are much worse than Macbeth's. Macduff, upon hearing this, cries out for his poor country and says all hope is lost. Then Malcolm tells Macduff that everything he just said was a lie meant to test Macduff's loyalty to Scotland. He knew that if Macduff made light of the sins about which Malcolm claimed to have, that Macduff just wanted to get Malcolm to come with him to Scotland. Since Macduff laments for his country's future instead, Malcolm knows that Macduff is sincere in wanting Malcolm to return to fight Macbeth.