Your contacts should already be saved to Google, unless you turned off Google sync. Go to contacts.google.com, log into your Google account and see if your contacts are listed there. Are you trying to edit from within the contacts app or the contacts tab in the phone app? If your contacts are in Google, you need to switch your location for your contact list to Google. Open the Contacts App. Tap the three-line menu on the top left, and you will see a list of actions. In the window "all contacts" should be showing with a count of all your contacts, regardless of storage location. Tap that window and it will bring up all the places your contacts are stored. You can choose Google as your default location. The advantage of storing them in Google rather than Samsung, is that your contacts can be accessed from any device or computer and transferred seamlessly from phone to phone regardless of brand. With Samsung you have to stay within the Samsung ecosystem to have access to your contacts. If you select manage contacts, you can transfer all your contacts to Google. That way if the edit function does not work within the phone, you can go to a computer and do your edits from within your Google account. So, you don't have to transfer them by hand.
Incidentally, I have never seen the edit option missing from the bottom of the screen. Have you tried deleting your cache partition? Something may have gotten confused with a recent update.
