Are you sure you don't need an apple account to buy stuff from the app store/iTunes - all iOS devices I've used have wanted apple account credentials to install apps, even free ones.
This isn't even really about Android: it's the Google Play Store, so you need a Google account to access it. It's the same as you'd use an Amazon account for Amazon, etc. You can use the phone without a Google account (just don't enter one), but then you don't have access to the Play Store.
Of course you can create a Google account for that purpose and use it for nothing else (or just that plus contacts backup, if you choose to sync contacts). Many do this. My only advice if you do this is to make a note of the account and password, as people who don't use it otherwise and hence only enter these credentials once sometimes forget them, which is awkward if you ever need to re-enter them (e.g. upgrade the phone or do a reset).
There's nothing that says you have to use Google for your email though - you can use Yahoo for that perfectly well.
Sorry if I've misunderstood though: I don't use Yahoo myself, so may have missed something.