Is it permissible to go to mixed swimming pools, taking care to choose times when they are free of women, or to non-mixed swimming pools where men do not cover themselves completely? And is it permissible for a man to wear shorts that reveal part of his thigh below the navel?

It is permissible to frequent a swimming pool designated for women, provided it is free of men. However, if there is a mixed-gender pool where men uncover their thighs, you must lower your gaze and offer them advice. It is not permissible to uncover anything below the navel, even slightly, as the area from below it down to the knee is considered 'awrah (private parts). The navel and the knee themselves are not part of the 'awrah.