Oem tyres are eurostar. The ones pre installed in city are very narrow. And One of the worst tyres available. They have a tendancy to skid as they are not wide enough. Thereby abs is activated more often.
Consider upgrading your tyres to 185/65/R15. Yokohoma advan DB preferred.
New oem tyres can be sold for 10,000 a set.
For your basic question, No it should never touch the ground. But, if you are braking hard and hit a speed braker then your front bumper can hit the braker if the braker is high enough. (The front of every car gets lower a bit when braking hard).