Yes, we use "意気投合" for any relationship not limited to romance. Age, sex, race, occupation etc. don't matter at all for "意気投合". ^ ^

You can use it, but if you use it to show relationships with opposite sex, some people might misunderstand that you have some affair with them. You might want to use it only to show relationships with same sex, but if you don't come up with any other expression than this, you'll need to explain the detail until the listener can see your intent.