Let me clear a point before starting,
We cannot blame the Tyre alone for vibration. Since there are lot of moving parts in cars.
They do have a good amount of contribution.
Now, Let me try answering your question,
Does Air pressure be a cause for vibration,
Yes, Both Low pressure and High Pressure cause vibrations.
The tire pressure plays a major role it but note here tires are interlinked to many components
such as Rims, wheel hubs, axle , suspension,brakes etc, So judgment should be liberal in this case.
Lets break down this topic to smaller piece,
Each tire type has precised tire pressure labeled on it so that it could perform optimally.
The air pressure should also be kept at a level which not only keeps the structure of the tire strong,but also includes some flexibility smoother bumps.
Low pressure in tires create more contact area in the road sacrificing the tire's structure.
Due to the changing mass of the car and shifting mass distribution it can be worse in handling as the structure shifting wouldn't be much faster as your car moves.
Also your weight shits to the the low pressure zone creating much pressure in tire.
That is why it become harder to steer the vehicle when the air is low.
Driving low on air pressures could even damage your tires walls. And its not recommended.
High Pressure tires can be compared to rock tires. Generally tires does some damping before it transfer to the suspension. So that's
why you notice the sensitivity of the chip-lets while you drive when the pressure's are high.
The reason why car topples on high speed is because tires looses its ability to shift the structure shape or we can say that it don't have the flexibility
to cope with the speed.
Only tires cannot be blamed for this reason. There are numerous other factors contributing to it.
Air in the tire play a major role as other components in the vehicle do. We often do ignore that. Because after it something that holds
your vehicle mass weight.
To better understand functioning of tire, take your car to a slop. Halt your car in such way that it should pick pace, turn off your engine, try to steer, it would be damn hard.
Try doing the same when the car is moving.
You will get the raw understanding of the scenarios how hard and easy was to steer when your car was unpressurized and over-pressured.
Tell someone to push the car and you steer it with engines off.
Note: Modern cars brakes don't work when engine turned off. Keep and on Parking brake/ Hand brake for emergency.
And regarding your other questions, I cannot answer it because choosing tires for vehicles is difficult part.
That depends on many criteria, just try check boxing the below fields and go for the tire it fits through,
- Type of road you drive - Highway, Country, off-road
- Your Driving Style - Rash, Rally, Drifter, Classic
- Weather conditions - Hot, Wet, Semi dry
- Comfort level - Superior, good, average
- Life - Descent, Should last my life time, Change it once with my grocery
- Warranty- yes - how much , no - never mind.
Small Tip: Dont just believe dealers, ask your friends which tires are they using. They don't need to have the same car because tire models they use could be available for other cars too. In the case of tires most of them are interchangeable
Hope this helps. Have a great day :)
Point to remember: Tyres are only point of contact for car to road, ground. Choose it wisely :) . Investing some time in research doesn't hurt you in no manner.