I have had to edit your question because it actually contained multiple questions. Please only ask one question at a time on enotes.
In this scene, Portia tells a rather confused Lucius what she wants him to do, which is to run to the Senate House. However, his lack of alacrity in responding to this command reveals how he doesn't really understand what his mistress is asking him to do:
Madam, what should I do?
Run to the Capitol, and nothing else?
And so return to you, and nothing else?
However, Portia, because of her premonition of the disaster that is about to befall her husband, wants Lucius just to go to the Senate House and check if Julius Caesar is well and how he looks:
Yes, bring me word, boy, if they lord look well,
For he went sickly forth; and take good note
What Caesar doth, what suitors press to him.
Thus Lucius is to check on the health and safety of his Lord, and thus satisfy the fears of Portia.