This depends on the vehicle, and whether you tow or carry heavy loads. The tyre pressure for most common cars including SUVs, people movers and personal utes, should be between 36psi and 40psi. Commercial vans (i.e. couriers) should be between 45psi and 50 psi. Electric cars should be 40psi due to the weight of the battery.
Between 10,000 and 15,000km after new tyres have been fitted, or when you find the front tyres are starting to have less tread than the rear tyres. At least once a year is a good way to keep track.
Every 20,000 to 25,000km, or if you start to see the tyres wearing uneven, wearing on one edge, if the car starts pulling to the left or right, or if you have hit a curb or pothole hard and the vehicle drives differently afterwards.
All tyre information is usually found on the side wall of you tyre. Here you should find: your tyre size - look for a sequence of numbers and letters that reads like "225.45R17"; the load and speed rating - it will follow the tyre size like "94V"; the brand and model of the tyre; the maximum pressure of inflation; and style of tread the tyre is - e.g. asymmetric tyres will have the word inside and outside and directional tyres usually have an arrow to show which way the tyre should rotate). The tyre will also have letters or symbols to say if it is a run flat tyre or not.
Many things can cause a car to shake. The main reasons are; tyre imbalance; uneven wear; tyre separation; an out of round or bulging tyre; flat spotting; and warped break rotors. In most cases you will start to feel a shake as the car reaches between 50-100km/h. If you feel shaking through the steering wheel, it is generally the front wheels, while if you feel shaking through the body or base of the driver's seat, it is in the rear. If you find you only get a shake or shudder under breaking, it is generally caused by the warped front brake rotors.