Thanks for that updated info. So we need to know a few things. If the option is there, it sounds like you are not using iCloud.
That being said, where are your contacts coming from? We need to check your settings to see if the Contacts account is set up through a third-party provider. This article will help: If your iCloud Contacts, Calendars, or Reminders won't sync
"If your contacts, calendars, and reminders are in iCloud, then iCloud automatically updates your information. If your information is in a third-party account, like Google or Yahoo, you can change your default account to iCloud. Changing your default account to iCloud won't move your existing information from a third-party service to iCloud."
Don't change it to iCloud, but find out where your contacts are coming from, and then if you turn off that account, you should be able to sync other info across then.
Music is similar. If you use iCloud, the option to sync manually may be removed, so it sounds like you might not be using iCloud for Music either. Use the Finder to sync your iPhone, iPad, or iPod with your computer
See the picture in that above article. If you wish to remove something, make sure that music is not selected. Let us know if you get any alerts or error codes. Thanks.