Caller options for iPhone 5c

I noticed the options on making calls are voicemail and call, is there any way to delete or hide the voicemail option on the iPhone 5c 32 gb phone

There is no option to make a voice mail call.

That is to check voice mails that others have left for you.

Go to your contacts, open a contact, on the far right will be two icons, one looks like a circle with a little tail, the other a phone, hit the phone and a call goes through, the other goes directly to voicemail. We tried this several times, hit the circle icon by mistake and that is what happened.

The little cloud you mean - or better 'text bubble' - as that is what it is.

It does not go to "voice mail", it sends a text message.

Voice mail - for those that have this service - is when you are allowed to leave a recorded "voice message" for someone when they do not answer their phone.