Congratulations on your new car!
To answer your first question I think it's really costly if you want to get it maintained by the company so its better to get it done from a reliable mechanic since that would be lighter on your pocket.
For the second question, you can expect around 5-6k just for oil and filter change. Not sure about tuning but even for that they charge a lot.
For the third question I would suggest getting all the fluids changed, this includes gear oil, oil and oil filter, air filter and cabin air filter. In addition, you may need to get the catalytic converter cleaned and for that a member on this forum can suggest you a good place.
Do have a look at the tyres and make sure they have enough tread and the brake fluid level to see if you need new brake pads.
After all this the fuel avg should go up to somewhere between 13 and 14 km/l. I hope your car serves you well!