Call your carrier or go into your local store. They'll sort out every single problem you currently are experiencing.
The reason your Gmail contacts got synced to your phone is because when you set up a Google account on your phone, which is used for email, the Play Store, call list, SMS, contacts and almost everything else on the phone (including a wide array of third-party apps), it automatically put all your email contacts on your phone for convenience. I understand you'd rather put your contacts manually into the memory on your SIM card, but doing it that way is extremely limited in terms of both feature set and total number of contacts. I 
think it's possible to unsync your contact list, though as I've always used Google's auto contact sync because I reformat so often, I'm not fully sure. SIM card contacts are also not as versatile as Google's account contacts and also won't be synced to your new phone when you upgrade unless you use the same SIM card, meaning you'll have to manually put in every single contact in again instead of having it synced automatically from the (secure) Google server.
Again, your carrier and local store will be able to sort out every issue you currently have. Enjoy the S4; I'm still with the S3 and while I love it I get phone envy whenever I see an S4. 
 
P.S. Google doesn't often provide direct support as the call volume from unhappy Android owners would be absolutely massive, as they control the lion's share of the current smartphone market. I hope that sheds a little light into that frustration! 
