Is there a connection between atheism and secularism; between agnosticism and secularism? Are the first two roughly synonyms?

Atheism and secularism are not synonyms. Secularism is certainly a result of atheism, but some claiming to be theists can be pretty secular in the way they live.

Well, I suppose if it's not (whatever "IT" is) religious, it's secular.

Atheism is the label we put on those that lack a belief in a god. 

Secularism is about governments that practice a separation between church and state. 

Agnosticism is the belief that God and whether he exists  is unknowable.  

None of these are synonymous, one deals with belief, one with knowledge, and the third we government and institutions. 

Inigo Montoya: You keep using that word. I do not think it means what you think it means.Dictionaries are your friend, don't be scared of them.

atheism is a religion, secularism is a way of government dealing with multiple religions.