Quote - 1) Once I save my custom morph, I can't save over it again if I make more changes to it (save over that same name). So how do I update it?

Spawn a new morph with a new name.

Quote - 2) Do I have to delete my saved custom morph from each body part one by one if I don't want it anymore?

Yes. When there are a number of morphs to delete, you may find it easier to delete morphs in the Hierarchy Editor than from the parameters palette. For a large number of morphs you may find it easier to delete them by editing the cr2 in "Morph Manager 4" or "CR2Builder", both are free.

Quote - If I select the "Body" and try to delete it from there, the "Delete Morph" option is grayed out, but I can individually delete my morph from each body part.

There are no morph targets in the Body actor, which is why you can't delete them. What you see in the Body are master FBM (Full Body Morph) dials. These just control morph channels, they are not morph targets themselves (they have no deltas). You can delete FBMs in the Hierarchy Editor, select "Show all parameters", then select the channel you want to delete, then press the keyboard Delete key. Deleting the FBM channel won't delete the individual morph targets.