How can I change the sequence of first and last name field in the block, witch comes up on Drupal's "Add new user" page's bottom. Now the sequence is first_name then last_name, but I should have last_name than first_name.
You can update the profile that is being used for registration by changing the weight of the field or using top/bottom arrows to change the order how they appear.
Navigate to Administer >> Customize Data and screens >> Profiles
Check the profile used for Drupal Registration and then click on the fields link besides it
Use the arrow button to change the order of the field.
You can also change the weight of the field by clicking on edit link of the field and then changing the order.