This shows how much Claudius cares about being King and holding onto his throne.
He knows that the public loves Hamlet, which is why he can't just arrest him for the murder of Polonius, he has to be much sneakier and trickier than that, otherwise the public will take Hamlet's side and Claudius will lose support.
This is false: it has a very negative connotation.
It refers to a smile that is mocking or contemptuous (or a remark that is mocking or contemptuos) - so it's not a genuine smile, but an ironic and sarcastic smile. It has a negative and not a neutral connotation.
In Act V, scene III of Romeo and Juliet, Paris represents an outside pressure that escalates a conflict because Paris wants to wed Juliet, but before they get to meet each other Juliet falls for Romeo. They get secretly married by Friar Laurence.
Her parents want her to marry Paris, he goes to ask to the same Friar to marry him with Juliet.
YES: Washington will forever be remembered for securing freedom for America.
YES: Washington embodies all the positive traits of a leader.
YES: The war has ended, and the British have been defeated.
On the other hand, these details do not belong:
NO: Motivated by Washington, citizens of other nations rebel against oppression.
NO: The attention he receives from world leaders inspires Washington to become a statesman.