Can Spectres do their Fell Light even after being charged?

No, fell light is during the move of the model, and they cannot move anymore when charged. Just like what happens with spellcasting.

OK...so ability to move affects this special rule? If a Spectre were surrounded by his own troops and could not move, he could still do it...
Or does the charge itself disable it ("he's so busy fighting")?

Most Special Rules, I think, are NOT affected by a charge, as magic casting is.

If the Spectre is surrounded by models and so is incapable of moving, he can still use his Fell Light Is In Them, only if he is engaged in combat can he not do so, because the fight "distracts" him so to speak.

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"I am the Flying Spagetti Monster. Thou shall have no other monsters before me"
-FSM.

Whilst there is a thread on spectres, can a spectre move a model and make them lie down?

Yes, I think, as it doesn't 'cause harm to the target.'

Can he do Fell Light even after being charged? Any other opinions?

The rule says "at any point of his move...". Charged models are not allowed to move.
Notice that if a modelis not able to move because of controlzones or something like that it still has a move (no matter his only choice is keep standing were it is) and therefore can do anything that requires moving (for example the mentioned special rule, or cast magic...).

So it sounds like a Charge actually cancels my opponents move...and therefore anything his model could otherwise do in the Move Phase.

Great! With over a hundred views and no other opinions, sounds like Spectres can NOT do Fell Light if charged.

Thanks all.

I hope you mean they can NOT

Yes, thanks: edited.