I think people are also slowly realizing that the service you're referring to, iTunes Match, is not a part of Family Sharing. It's a huge bummer but I'm sure they'll provide it to Family Share accounts in the future.
Nooo, you can stream purchased music from your account without downloading it. That got introduced in iOS 7. Same thing with movies and TV shows. iTunes Match basically is for adding your ripped stuff to your purchased list and allowing remote playback without it being on the device.
I am having the same issue trying to let my parents watch my stuff on their iPads. Now it works streaming ANYTHING on Apple TV, but as far as I can tell on iPads and iPhones you have to download music, TV shows and movies. You obviously would have to download apps, but I've heard that IAPs aren't accessible that way.
I don't get why Family Sharing isn't built into the Music and Videos apps the way it's built in to those same apps on Apple TV. The way it works is obviously better than not working, but I sure as heck don't feel like hand-holding them through downloading songs, playing them, removing as needed, blah blah blah. I've put a password storing app on my dad's phone, iPad and computer and he still won't just look up his damn passwords instead of resetting them, which if you've ever reset an Apple ID password, AUUGGGHHH.
So after I get my new phone and it still doesn't work, I'll probably just find a way to send Apple an email about it and suggest that feature. I also wish I knew how to share only certain media because I'd like to share a few movies and TV shows with my nephews. I'm fine with sharing some TMNT cartoons with them, but I don't think they need access to the unrated edition of "American Pie."