Do people actually believe in this stuff?

yes i think people these days still believe in stuff like this as they believe it will come true and its possible. i remember reading some article why indian rain dance is so powerful, it says because they never stop dancing till it rains, so in the case of these farmers i think doing this practice is proven by their ancestors, they didn't stop marrying off frogs till they have the monsoon rains before, so they are doing it again.