Is it possible to install an Ubuntu server on Gigarocket and then on that server install some application, so it can be reached from Internet?
No it is not. GigaRocket provides shared hosting only. You will need a VPS or dedicated server for what you want to do.
It's a shame, because from what I can tell, you used to provide free VPS and still have a page saying you do, but then later I find info saying you don't anymore. This website could do with a bit of tidying to make it clearer to all us newbies.
You can connect to your shared hosting with ssh but you don't have the shell access , cause this is the shared hosting with one static IP and many sites which hosted with it.
If you want shell access to install scripts and editing the OS , you can buy dedicated private server.