Magento 1.9 – How to Remove Last Name from Checkout Page

It's possible via layout XML

In your theme's local.xml, add the following lines (before </layout>):

<customer_account_create>
  <reference name="customer_form_register">
    <action method="setShowAddressFields"><value>1</value></action>
  </reference>
</customer_account_create>

If you don't have a customized theme but a bought one, you should create a child theme for customizations like this.

Example

For the Ultimo theme, the theme resides in app/design/frontend/ultimo/default (Ultimo is the "package", "default" the theme).

You should then create the directory app/design/frontend/ultimo/yourname/layout and add a file local.xml there:

<?xml version="1.0"?>
<layout>
  <customer_account_create>
    <reference name="customer_form_register">
      <action method="setShowAddressFields"><value>1</value></action>
    </reference>
  </customer_account_create>
</layout>

Then configure the custom theme:

Answer to updated question

It's a totally different question now. To allow saving the telephone attribute of the customer in the registration form, you need to tell Magento that it is allowed to be used in that form (this was introduced in Magento 1.5 to prevent customers to modify arbitrary attributes that are not meant to be changed by them).

Write a setup script (as part of a new module, or an existing one if you already have a custom module dedicated to theme and configuration) which contains the following:

Mage::getSingleton('eav/config')
    ->getAttribute('customer', 'telephone')
    ->setData('used_in_forms', array('customer_account_create'))
    ->save();

^{Source: http://www.schmengler-se.de/en/2011/03/magento-1-5-neue-kundenattribute-im-backend-fomular-sichtbar-machen/}

You have to add else statment if the user is not uploading for the edit. $postdata['file_path']['value'] this is created by Magento automatically.

if(isset($_FILES['file_path']['name']) && (file_exists($_FILES['file_path']['tmp_name']))) {
    // something ....
} else {
    $postdata['file_path'] = $postdata['file_path']['value'];
}