I have heard that ruchot, shedim and mazzikim don’t exist in Eretz Yisrael. Is this true?

The Gemara in Pesachim 110b teaches that in Eretz Yisrael some of the customs dealing with the phenomena you mention were not observed. Rav Kook (Shu"t Ezrat Cohen 6) writes that this is because the sanctity of the Land of Israel protects one against damaging influences. Babylonia, that had been home to Nebuchadnezzer was particularly plagued by mazzikim; in Eretz Yisrael the problem was minimal.