Most of the feminists I know are straight and either married or partnered - they clearly don't hate all men. Some maybe do, but I don't think it's the majority.
I don't know where this is true, but certainly not in Western countries, where such discrimination by gender is illegal.
I'm in the US and it's absolutely endemic. Women still make significantly less than men on average and gender discrimination is baked right into jobs. My city starts teachers at $56k and police officers at $70k - one of those jobs requires a GED and the other requires a Bachelors degree. Even with a Master's teachers can make as little as $61k - and that's entirely because it's traditionally a "women's job". Can you name any male dominated field where most workers have a master's degree and make that little?
Europe's maybe a little better, but there's still no country where women outearn men - if there really was equality there you'd expect to see that look more like a bell curve.