When you land at the airport in Zagreb, the best option to get to Karlovac the bus or train (price is around 40HRK/5€) because it leaves you in front of the venue. When you arrive at the airport the best way for you is to call taxi to take you to the main bus/train station in Zagreb, as the airport is a bit away from Zagreb. When you get there, buy a bus ticket for Karlovac(if you go with train, buy ticket for Karlovac Centar station).
besides gaming, is there anything cool to do in/near karlovac (or zagreb) during this period
It depends on when you arrive and leave. On tomorrowlan we arrived the day before the event started and we had plenty of time to go to a bar and drink some beers with people and have dinner with other teams. Also if you go out of groups on day one you'll have time off the 2nd day obviously.