"According to Ockham, everything in external reality is singular". This is not a good way of characterising Ockham's nominalism, for it could equally apply to some of the brands of realism which he criticises and caricatures. For example, a realist who holds that a universal is a singular thing, inhering in some way in many things, also holds that everything (including universals) is singular. But they would clearly not be a nominalist.
A similar observation applies to the so-called Ockham's razor. "Do not multiply entities beyond what is necessary". Sure, but realists agree with that too. The disagreement is over what counts as necessary. Realists would hold that universals are necessary, of course.