During my studies, I have to make a project connected with programming in Java. I learn Java from a few months and I would like to make something interesting (not an application for bank, library, car renting etc). I'm wondering whether it is possible to create real-time web game/application, where you can type something and your friend on another laptop see this message and can send you response? (using internet/Bluetooth) If yes, what I should look for to find information about this type of applications?
Yes, creating something like this is definitely possible. It really will just depend on exactly how you want to implement this (it sounds like you're still not sure EXACTLY what you want, as your description is vague).
What I mean by that, is what do you want as your medium? Would you like the two users to be on their laptops and communicating through their web browsers? Or would you rather have a standalone application that accomplishes this? If so, what Operating Systems will you support? Will it have a graphical user interface, or will it run on the command line?
Let's assume that you want to develop a standalone Windows application that allows the users to exchange messages. Keep in mind that doing this gracefully would involve users logging into your system with authentication, a fairly sophisticated GUI, and lots of encryption for privacy reasons. That being said, a very basic implementation of this could probably be as follows:
You'd have an app that runs locally on the users machine, and also some sort of database backend that your app communicates with. I'd recommend using a mySQL database hosted by Amazons RDS (Here's a tutorial that got me using Javas JDBC library to work with an Amazon RDS database - https://www.youtube.com/watch?v=2i4t-SL1VsU).
Rather than worry about a GUI, I'd suggest trying to get your prototype working on the command line. Your app could preform the following steps when booting up:
You can see that this would accomplish a very crude version of what you asked for, and the devil is in the details. I'd suggest building something very simple like this, and then adding functionality by tweaking and improving features one at a time.