How to fix the Google Plus? Please help.

Okay so I have an email in my phone. I deleted it. And I found out that Google Plus didnt work. So I added another Gmail email. Now Google Plus works, but whenever I try to update apps, it says something like ” Authenticiation failed. You need to be logged in.” And I tried to delete the Gmail account that I already deleted out of my phone, but it says “Some applications require this app. Do a Factory Reset.” I don’t want to do that. So how do I fix this without a factory reset? I want to update Kakao Talk. Please please help. Thanks.