Am I allowed to discard cards at any time, even if I am not compelled to do so?

For example, if Varys is already played and I have him on hand, may I discard him before the strategycard "Heads on Spikes" is resolved? To prevent the opponent from getting 2 power...

And if so, to which point may I do it? Even after it being revealed? Or do I have to discard him before I know if the opponent played Heads on Spikes?

Also, may I discard characters, items or locations that are in game under my control?

No, you may not discard cards from hand or from play unless allowed/forced to do so by a card effect.