Strong and Weak Acids/Bases I'm so confused... $\ce{HClO}$ is a weak acid. then why is its conjugate base, $\ce{ClO-}$, a weak base in water? shouldn't they be inversely proportional? shouldn't $\ce{ClO-}$,  be a strong base? 

If $\ce{HClO}$ is a weak acid, that means it does not readily give up a proton and has a strong pull on them. So when it becomes a conjugate base, $\ce{ClO-}$, shouldn't it readily take protons and therefore be a strong base in water? 

ALSO,
when an acid is dissolved in water, and some of that acid dissociates into $\ce{H3O+}$, is the Kw of water negligible and you only consider the Ka when finding pH? But that confuses me because I thought you use 14, the exponent of Kw when finding pH.
$K_\mathrm a\times K_\mathrm b = K_\mathrm w$.  Some teachers tell their students that the conjugate base of a weak acid is strong but it's not true.  What is true is that the stronger the acid, the weaker the conjugate base and vice versa.

Yes to your second question.  When calculating the pH of a solution, the hydronium ion concentration is usually controlled by the strongest acid in the solution.  This is the case in the type of problems found in lower level chem classes.  In a higher level class problems with acids close enough in strength so that both acids matter may be encountered.