Disclaimer: Ok, in my first two paragraphs I will just assume that you know very little about the works of a network. If you find these to be child play just overview them
Well... technically you can be hacked because of the mere act of connecting to your ISP (opening your connection). Normally this is not likely, and the only reason your chances of getting "hacked" increase when you surf the web is because you are constantly yelling out your IP address to the world. (when you download something from a server, you need to tell the server your IP address so he can answer you back. In this communication is when a malicious user can get your address and misuse it...).
Now on the Internet part, when you use Kalleira you are connecting to the Internet. The www, or the web as it is commonly known, is just one of the services the Internet offers. The Internet is nothing more and nothing less than the sum of all the public networks that exist in the world. If you connect to a public Kalleira server you are connecting to the Internet.
Of course when connecting to the Kalleira server your chances of getting hacked will increase, because of the fact that you are telling every machine on the server how to connect to you. However, this is not likely, and I wouldn't worry too much really...
If you are still worried, you could still do some simple things like getting a firewall (Tiny Personal Firewall is the easiest to use I've encountered so far), shutting down ports/servers that you don't use, etc.