I'm not sure about your family dynamics, so I don't know how much help I can be there (unless you would feel comfortable sharing more details) but as far as your account and downloads, perhaps try using an app that mimics another (I have one that looks and acts like a calculator until you put the pin in it) which can hide apps, photos, files, etc.
I'm sure there is also a way to change the app icon (it's relatively easy on a desktop computer, although I'm not sure on the specifics for mobile devices).
From what I read in the terms and conditions and rules (someone correct me if I'm wrong), you are allowed to use a VPN or proxy server after creating your account. So, you could always use TOR to prevent your parents from viewing history, ect, combined with the above point to keep them from finding the TOR app.
Even better, if you have a computer and a hard drive, you can try the TAILS operating system. It's basically a portable operating system and is heavily focused on anonymity.
The only thing is that if they know your username, they can still look you up and find you active, and since you're only allowed one account, I'm not sure how to work around that.