The issue here is that the user's permalinks are not working after migrating their site resulting in a 404.
Solution:
It would appear that your permalinks need to be reset. Can you go to your backend and click on Settings -> Permalink and set the permalinks to default.
Once you've done this check again on the frontend to see if the pages will now load with the default permalinks. If they do go back to Settings -> Permalink and then change the permalink settings back to Postname.
Problem:
Display last 2 article in Archive Page - last 2 items are missing.
Solution:
The issue was you set your pagination to display 10 results per page but actually you are using 3 column grid so to fill the gap I set the pagination to use 12 posts per page and now its displays the expected results.
