I'm writing a high efficent server with which my application will be communicate. The server will work using TCP/IP on port 80. I have a question about firewalls : if some user behind the firewall can use web browsers to navigate web pages then he can use my application too without any problems with transfering data?
That all depends. If the user lives outside your firewall then yes. However, if the user lives inside your firewall, your DNS authoratative server is outside your firewall, and your internal client tries to access, it may not work.
Hope that makes sense to you. But most firewalls will not let a user out and then back in on the same connection.