Wa Alaikum Salam Brother. First of all, Heartiest Congratulations on the purchase of car! May ALLAH ALMIGHTY Bless you more, and you drive it more and more, and enjoy its comfort and ride in the years to come. Ameen. Do give some charity too!
There is no one as best or worst. It all depends on one's personal experiences. Vitz is not an out of market, or rare / vintage / classic car. Even in your locality, you will find many garages. Just visit the market, conduct survey, ask shopkeepers. 3-5 will refer to a same, good and reputed garage. Visit it, have discussion with the mechanics and you are good to go. Just ensure that they have right tools to do the jobs.
Only genuine, OEM one! It will cost somewhere in-between 2500-2700 PKR, and will easily last 10-15,000 Kms, with condition that it is regularly cleaned with pressurized air. Otherwise, Leppon! Cost: 600-800 PKR, and lasts 8-10,000 Kms. Cleaning also required here, in fact for any air filter.
Of course you can! It only takes a minute or 2.
Immediately switch to 100% genuine and original, 5w-30, API SN / SN Plus, Fully Synthetic engine oil from any reputed brand. 10w-40 is thick oil and not a recommended oil grade for 1KR-FE.
For best for bucks, use Total Quartz 9000 Future Series (or latest compatible available) and change along with genuine, OEM oil filter after every 5,000 Kms.
Yes, whenever you feel decrease in pick, power, fuel efficiency and performance. It may not be required now, but after driving your car for 10-15,000 Kms, you may require its cleaning. Bad quality of fuel here chokes Catalytic Converters very easily and early.
Its part of engine tuning. Tuning of current EFI engines usually involves: Throttle body cleaning / service, spark plugs cleaning / replacement, cleaning / replacement of Air Filter. Of course, engine oil change along with oil filter is mostly there, at the time of engine tune-up. For "what is throttle body?", you may Google.
I hope, all above helps. Thank you!