With an allosteric inhibitor (AI), you mentioned that either Vmax or Km can be changed. Then can I say that the apparent Km will be the average of the weakened enzyme molecules and those remaining uninhibited, thus the apparent Km will increase?
From its remote binding site, an AI could affect the shape of the substrate binding site, thus changing the binding affinity andthe apparent Km. In a mixture of inhibited and non-inhibited enzyme molecules, I would expect the Vo vs. S curve to be complex (biphasic?) and not yield an "average" Km.

Allosteric inhibition (AI) can be similar to either CI or NCI. If after the AI binds to the enzyme on the allosteric site, the active site of the enzyme is so distorted that S can not bind, then effectively AI serves as a "competitive" inhibitor. And it will only affect Km but not Vmax. Am I right?
It affects Km in a manner different from that of a competitive inhibitor, since it binds at a different site. It is changing the Km of the enzyme by "changing" the enzyme. Actually it brings about this change by stabilizing a natural alternative inactive state of the enzyme, see Purves tet, p. 129-130.

NCI and allosteric inhibitors seem very similar, but why do NCI leave Km unaffected but allosteric inhibitors can affect Km?
Non-competitive inhibitors do not affect Km by definition.

Is allosteric inhibition "all or nothing?" That is, compet. inhibition isn't all or nothing: if you add enough substrate you mask inhibitor's effect. What about Non-compet. inhibition? How would you classify that?
None of these inhibitions is all-or-nothing when considering a population of molecules (which we almost always should do). At certain intermediate concentrations of inhibitors, you always have partial inhibition overall.