He knows them well and is clever; he can tell because they are acting guiltily.
In England where they have been sent to accompany Hamlet to his death.
They are Rosencrantz and Guildenstern.
Claudius sent with Rosencrantz and Guildenstern an order to the king of England to have Hamlet put to death. I assume this is the "murderous commission" you are talking about. Hamlet finds it and substitutes another which is worded just the same, except it is Rosencrantz and Guildenstern who are to be killed, not Hamlet.
They are. If they weren't, Hamlet wouldn't have sent them to their death. They had the opportunity to betray him when they were out of his sight. It seems the king didn't completely take them into his confidence, though, so perhaps their loyalty wasn't total.
Rosencrantz and Guildenstern ultimately meet their demise when they are sent to England with a letter ordering the execution of Hamlet. Unbeknownst to them, Hamlet discovers this plot and alters the letter, leading to the execution of Rosencrantz and Guildenstern instead. Their fate underscores the themes of betrayal and the tragic consequences of manipulation in Shakespeare's play.
They were sent for specifically to spy on Hamlet and report to the king and queen. Spies generally do not like the people they are spying on to know it. Rosencrantz and Guildenstern would have an easier time getting unguarded admissions from Hamlet if they were not "outed".
The king and queen want them to cozy up to Hamlet and find out what's troubling him.
Rosenkrantz and Guildenstern. Personal note: I have met the actor who played one of these roles in the original stage production.
Certainly not. They were not even in Elsinore until well after Hamlet was visited by the Ghost. Then they were "sent for" by Claudius to find out what was up with Hamlet.
Claudius sends Hamlet to England after Hamlet kills Polonius. However, Hamlet's ship is intercepted by pirates and Hamlet is able to talk his way on to their boat and back to Denmark. Rosencrantz and Guildenstern remain on Hamlet's boat and land in England, where they are executed.
Hamlet does not reveal much to these two. They go to him in order to find out about where Polonius has been buried, but they do not get many answers.
Hamlet's ship was attacked by pirates. The pirates agreed to return Hamlet to Denmark for a price. He sent word to Horatio and asked him to get ready to meet him. We also learn that his traitorous friends, Rosencrantz and Guildenstern, have met with some dire circumstances.