The elusive particle "ne"

This ubiquitous little word has several meanings and usages, none of which seems to correspond exactly to any Eng. word or phrase. Here you can find a series of examples, listed according to the general area of meaning.
Before vowels, "ne" is shortened to "n' ".

Quantity / Existence

"Quante mele desidera?" "Ne vorrei quattro" ( How many apples do you want? I'd like to have four [of them])
"Fumetti anni '80 ne avete?" ( Comics of the eighties - have you got any [of them]?)
"Fantasmi in questo castello? Non ce n'è nemmeno uno" ( Ghosts in this castle? There isn't even one [of them])
"Abbiamo tanta birra: ne vuoi?"( We've got a lot of beer: would you like to have some [of it]?")
"Hai delle arance?" "Ce ne sono tre kili" ( Have you got any oranges? There are three kilos [of them])

Movement

"Se ne andava nel parco sola soletta" ( She was going into/about the park all by herself)
"Sono stufo! Me ne vado!" ( I'm fed up! I'm going away!)
"La stazione? Ne vengo adesso e non ci sono ritardi"( The station? I'm coming from there now and there are no delays)
"Vattene! Perché non vuoi andartene?" ( Go away! Why don't you want to go away?)

The last example shows that "ne", too, can be affixed to verbs - see

Origin, source

"Se ne deduce che Omar era innocente" ( From that we can infer that Omar was innocent)
"E' un teorema importante: ne derivano molti corollari" ( It's an important theorem: several corollaries derive from it)

Topic

"Mi spiace, non ne so niente" ( Sorry, I don't know anything about it)

"Me ne frego!" "No, non puoi fregartene" ( I couldn't care less [about that]! No, you can't ignore that)
"Non ne dubito" ( I have no doubts about that)

What's the difference...

...between "Adesso vado a fare la spesa" and "Adesso me ne vado a fare la spesa" ( I'm going shopping now) ? The former is plain, factual information; the latter implies some kind of overtone - it can be an expression of protest, relief, satisfaction or other feelings, depending on the situation.