I own the same model vitz and what i m sharing with you is my personal experience.
Regarding the tyre size for this model, the oem recommedations are 165/70/14 but due to the ground clearance issue, people mostly go for bigger sizes. I am personally using 185/70/14, although compromising a little on fuel avg. As i am getting 11.5 to 12km/l in city with ac and 14 on long routes with ac. with this tyre size but still having a great experience with drive nd grip. Have been using yoko blueearth es32 series for the past 2years.
If you have no budget issue, go for yokohama, bridgestone or dunlop. Would do the job perfectly for you.
Regarding engine oil, 5w30 is the recommended grade as per oem. Any reputed brand would do the job like caltex havoline, total quartz etc. but make sure it is meeting the Api Sn/ Sn plus or ilsac criteria. Leave liqui molli, too expensive and no need as it ain't any racing car or some mercedes/audi.
1krfe is notorious for noise. You have to live with it. But make sure you are pouring the right engine oil, as i mentioned above as it has alot to do with the engine noise.
Check the cat converter, whether is is present in your car or not. Nowadays cat converters are being removed instead of changing them when choked and you wont notice it until you check it. If absent, it increases the exhaust noise.
