jasper reports server?
Is this scenario plausible with current jasper reports software (open source or similar), 

Yes. 

could it be done 

Yes.

and what would be steps in the right direction ?

Write a web server in Python.  Your web server will allow a user to enter information on a web site and after submitting, data would be transfered to jasper reports server and pdf would be created.  Your web server would provide the PDF back to the user.
You need to pick a framework, install the components, write the unit tests, write the code, debug the code and transition the code to production.
It's hard (given the question) to determine what part of this you actually need help with.
I would like to generate reports in pdf format with following scenario: people would enter information on a web site and after submitting, data would be transfered to jasper reports server and pdf would be created.
Python would be language of choice for my task.
Is this scenario plausible with current jasper reports software (open source or similar), could it be done, and what would be steps in the right direction ?