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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
When Malcolm is named heir to the throne.
Malcolm's title is Prince of Cumberland. He is named Duncan's heir apparent. At the time, the eldest son was NOT automatically the next in line for the throne. Macbeth, as the most experienced and respected soldier, expects to be named, but Duncan passes him over for the feckless Malcolm.
Macbeth has "black and deep desires" regarding dutchman's son and heir, malcolm.
There is no indication of any closeness between them. Macduff is never much interested in socializing with Macbeth. We first see him when he arrives at Macbeth's castle to see Duncan. Note that it is the king he wants to see, not Macbeth. When Macbeth is named king, Macduff refuses to attend the coronation. He also refuses to come to Lady Macbeth's dinner party. It would appear that he never liked Macbeth much.
The "black and deep desires" he is talking about is the temptation to hurry along Duncan's death so he can become king quicker. At this point because Duncan has nepotistically named his son as his favoured heir, and so it looks like Macbeth won't become king just by waiting for it. The temptation is to help the prophecy along.