I understand that lying is Assur, but is permitted in certain situations. 1) Is it permissible to lie for the sake of tarnishing the reputation of the enemy (such as against Hamas for propaganda reasons)? 2) Is it permissible to lie about Israeli casualties etc. for the sake of gaining support for Madinat Yisroel?

Thank you for your question, There is no need to lie about any of this. The real bonafide facts will definitely cause anyone who is honest to support Israel. Additionally, it is a bad idea to lie because the truth will come out and the lying will backfire. The real reason that many of the nations around the world don’t support Israel is because they are antisemitic, as Chazal said הלכה היא שעשו שונא ליעקב. Meaning that the non-Jews very often hate Jews throughout the generations. All the best!