How I can do some operations like for example filling forms on the other website using PHP or JS/JQuery ?
just use html no need of php/js make a form and use method="post" and action="www.url.com/login" and use
<input id="yourid" name="same_as_in_the_website" value="your_data_eg.mailid">
It would be messy complicated but likely but not definitely possible.
Why "not definitely possible" ?
Assuming there are no limitations preventing you from posting data to the server, then you could create your own webpage that performs the same functions as the original (asks and posts the data).
Alternatively, you can have PHP post the data, server to server.
The fact you are asking this question leads me to believe you are less familiar with programming. The risks of you mis-using the solution and possibly performing a DoS attack on a remote server cannot be ruled out.
I suggest you dip your does in to the worlds of programming with some simple javascript and html5 work prior to moving on to submitting form data to server.
You can make a value attribute for the input or textarea element or you can do it with JS with a document.getElementById.InnerHTML = ("....") i think