Show "create new node" form with "my" and "user I followed" content in a single block
I have a content type. Let us say "articles". When a user wants to
  create an article, he will go to /node/add/article and it will show a
  form like it shows on stack exchange when go to /questions/ask.


Give whichever user you want to create the node, permission to do so /admin/people/permissions

What I want?



  I want to create a block which will show the "create new node" form
  as above
  
  
  my articles
  


You mean the articles of admin or of the user creating the form? If admin, create a view with articles and filter by user admin, or filter by currently logged in user.


  
  articles of the user I am following with follow(user) flag.
  


as above. I presume you are giving the user the ability to flag other users to follow somehow? So you could filter by a list of users that are being followed.


  "My" and "user followed" articles should be shown below the form. The
  form and articles should always be visible in the block.
  
  When user saves a new article, it should show in the list below
  without page refresh.


You would use ajax to achieve this. Check out 'exposed filters' in views and look for the option to 'use ajax'.


  The user should not be allowed to select text format. The admin should
  choose which text format to enable on this particular content type.


This is built in. There are permissions for, example, "Use the Filtered HTML text format" and in the settings for the content type, which text formats are available.


  Note: When user visits node/add/articles directly, he must not see the
  articles. He should only see the form to create a new node.
  
  I am sure I have explained it quite well. Let me know in case you have
  any questions.


There are multiple questions here, and ideally you would post some code and show what you have already done.