Answers for "can radio buttons be checked all times"

uncheck all radio buttons

$('.classname').prop('checked', false);

check if one of the radio button is checked

if ($('input[name='+ radioName +']:checked').length) {
           // at least one of the radio buttons was checked
           return true; // allow whatever action would normally happen to continue
      }
      else {
           // no radio button was checked
           return false; // stop whatever action would normally happen
      }