I want to save and view the node content in the same page without page refresh using content types
Here I have some material for you that will help you to save node form through ajax without refreshing the page at https://www.drupal.org/node/752056 . Here is also another link that will clear your idea about ajax enabled form at https://www.drupal.org/node/264429 .
The solution of second part of your question that shows the node value is so simple. Just make a block views containing your required field from your selected content type and then place that block into your current admin theme at desired region. Don't forget to apply restriction to only show to specific content type.