So first, Yahoo!'s response to me was very simple. They are currently in the process of changing security protocols due to recent hacking issues. At this time the option was take the server down or to turn off the Push capability. They assured me it would be back on and did not say a word about downloading the app.
This did however say that unless you need an email instantly, using Fetch is easier on the battery. They said, is like a constant checking of "Is there mail, is there mail, is there mail" consistently at all times while Fetch at 15 minute intervals will increase battery life, but for those who need instant notification Push will be back probably with iOS 11.
So here's the weird thing. In an attempt to get PUSH back before my correspondence I deleted all my Yahoo and Gmail Accounts from my iPhone. My Yahoo!'s load in the native app perfect. My Gmails are not budging. I enter the username and password and it flash back to account screen where you choose and email provider.