I have a proxy internet connection. However some applications I need to run that do not work under proxy, and require direct connection. Is there some way by which my proxy connection behaves as direct connection?
If your proxy is based on SOCKS, then see this question: See this question: Is there any utility like `Proxifier` for Ubuntu?
If it is HTTP, you're out of luck. HTTP proxying does not support arbitrary applications, because HTTP proxying is transparent to clients, but requires server support (namely, the HTTP protocol which supports proxying inherently).
If you have a HTTPS proxy, which allows connections to arbitrary ports, evidently there is way to use it for arbitrary connections. RFC2817 describes a CONNECT method in section 5.2 which establishes a generic TCP tunnel.
SOCKS proxies are transparent to servers, but require client support. Clients are either written to do their network-related calls to a SOCKS library instead of directly to the operating system's socket library, or else a proxifier is used, which is a program that intercepts the network-related library calls made by the application's executable. This is what the above question is about: what proxifiers are available on Ubuntu.
If you're seeing other people on your network use arbitrary network applications through the proxy, that suggests your proxy may be SOCKS and that they are using proxifiers. But of course, if those users are on Windows, then what they are using isn't applicable for GNU/Linux.