Guys I found the answer.
Well, after a lot of changes in codes, I finally did it through API.
Through that PHP page, you can search in any plugin which exist in Wordpress Repository.
Sorry, I cannot include the code because it's too long.
Basically, I am just listing down in short what exactly I did.
First of all I included a PHP cURL script through CallAPI function. (I copied the same script which is included in the most-voted answer of this question: https://stackoverflow.com/questions/21182946/using-curl-to-get-api-data-within-php)
Then, I added actions and requests to that PHP script as explained here: http://code.tutsplus.com/articles/interacting-with-wordpress-plug-in-theme-api--wp-25805
After this, I unserialized the execution of the CallAPI function
Through this, I got all the info that I needed.
Finally, I then made a table in foreach loop so that details of each and every plugin will show up by loop according to what I wanted to show.
For eg: I only wanted to show the Name, Author, Plugin Version and Downloads. So, according to that I changed the elements of the table.
Through this, I can see 25 last updated wordpress plugins on opening that PHP page and when searched, I can find out any plugin from the Wordpress Repository.
The only thing which is missing is live AJAX search which I am trying to implement now.
Hope this explanation will help you guys.
After shortening that code, I'll add it here. (If possible!)