Question

What does hamlet think of rosencrantz and guildenstern? why must the king "not put the strong arm on" hamlet?

Answer 1

That depends on when Hamlet might be thinking of them. The reader is told that the two characters are friends of Hamlet, most likely the same way that Horatio is friends with Hamlet. So at one point Hamlet likes these two guys. 

The problem though is that Rosencrantz and Guildenstern abuse their friendship with Hamlet. At least that is how Hamlet interprets it. At the point in the play when Rosencrantz and Guildenstern show up.

Hamlet's mother truly loves him and would want no harm to come to him, and the people of Denmark love him and would be uneasy if something would happen to him.