There are a few adjectives that end in -ой instead of -ый in nominative (and accusative) singular. Maybe that is what's confusing you? Other examples are большой and плохой.
I'm not completely sure, but I think all of these are end-stressed.
No it's nothing to do with hard of soft (although -ой is always hard). Joke was right that's it's the form used when the ending has to be stressed. Interestingly I assume this means you can't have end-stressed soft adjectives in Russian.
The adjective agrees with the noun it describes in gender, number and case: the noun "футбол" is masculine singular accusative, so the adjective "мужской" should be masculine singular accusative as well.