Is it permissible to shoot coins (pennies, dimes, quarters) at a fox using a slingshot? Or would this fall into prohibitions of Tzaar Baalei Chayim, Bal Tashchis, or general Derech Eretz? Thank you for any answers.

ב"ה Shalom, Shooting coins at a fox for no practical purpose is surely Tzaar Baalei Chayim. According to many Rishonim causing pain to an animal is a Torah prohibition. This is also the opinion of the Rema in the Shulchan Aruch (Choshen Mishpat 272:9). You could add on that this is also something which lacks Derech Eretz, from the fact that a person doesn't aappreciate Hashem creations and wants to cause them harm. All the best