First thing is that you can create,edit or delete provisioning profile (developer,distribution) or certificates which wont effect the apps already live (on app-store). But it will effect the apps that you are using in your current project for testing in Device.
You can Delete all provisioning profiles and certificates. But you have to create again for testing your app in to device as well as upload new app on app-store from iTunes connect.
Apple provide Very nice and clear documentation please read bellow link for more clear
Provisioning and Development
Push Notification
The push certificate cannot be renewed. You have to create a new one.
The push notification certificate is not part of the application build. Therefore for push to continue working you only have to create a new certificate and deploy the p12 file (or whatever other format you are using) at your server. You don't have to submit a new version of your app.
Regarding refreshing the accounts and provisioning profiles, check here and here.