Is it possible to allow customer to mark his order as delivered on the order details page?

RE: "... the code for MARK AS DELIVERED button for front end ... "
If you are expecting that you can do this feature by only modifying the .cshtml page,  then  you will be disappointed.  Although razor code can probably 'resolve' the services you need to get the Shipment Id, the button needs to 'submit' to a controller action to update the shipment status (which will then updated the order status.)

New York wrote:

So how to be in this case? :))))

New York wrote:

Is it possible to do it with a separate plugin?

yes it can do by customize and by creating a separate plugin
its all up to your equirement

Yes, a custom Widget plugin would probably work best.  (The widget would contain the button, and could be placed in a 'zone' on your existing .cshtml page.)