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If the state gives money from your taxes to you, or waves that amount for you in return for what you gave of zakah or charity to charitable organisations, then the money that comes back is yours, and it does not affect your zakah.

Your going out to deliver the Jumu`ah khutbah in another mosque is permissible, because your i`tikaf is sunnah and recommended (mustahabb) – and not obligatory – but it renders your i`tikaf invalid, unless you stipulated that you could go out for that purpose before starting your i`tikaf.