Can't read form values

Remove the enctype="multipart/form-data" attribute from the opening form tag

That attribute is only needed when uploading files.

I missed this up untill now, but that indeed could be the cause.
If you do require uploading files in the future, you will need to do this;

Code:

function save(form) {
   // NO!!! Don't do this!
   var formData = $(form).serialize();

   // YES!!! Do this!
   var formData = new FormData(form);

   $.ajax({
           url: url,
           type: "POST",
           data: formData,
           dataType: "JSON",
           ......
           ......
}

Sir, 

But for now, I just need input text and removing the enctype="multipart/form-data" doesn't change anything. My idea of creating a one-page CRUD in codeigniter seems too hard for a beginner. If I can't correct the errors I may use the modal way but as this moment I will stick on one-page crud. 
Thanks for the TIME.

1. new FormData(form); is the new way, but the old way do it too (.serialize())
2. the ajax method does not know about multipart/form-data. It does not care about it.

You have only one problem. you does not know how to debug you code
Use the developer console. Every browser has a developer console.

if you send the ajax request, check the developer console. In the network tab you see an entry. Make a screenshot from it.