"Call" meaning "make a telephone (or radio, or Skype etc) call" is transitive.
"Call to" is only used used literally, in the meaning "raise your voice so that somebody not close to you will hear you".
"Called them up" is possible, but to me reads a little oddly. It suggests that there was a more purposeful or intentional nature to the calling, but the suggestion is only slight.
"No one answered" seems more natural here, but "no one has answered" is possible - it implies that this has only just happened, and you are still in the aftermath of the failed attempt. In that case "I have called them" would be natural.