You need to check the specification of the interfaces.
Arduino works typically with 0 and 5Volt (this is called TTL level). Sensors can do this too, but they can also be 3.3 volt which means you might need a voltage convertor.
Sensors are spoken to in a certain protocol. That can be as simple as an output voltage between 0..5V (e.g. LM35 temp sensor) which can be connected to an Arduino Analog pin. Or it talks rs232 (TTL level other higher -> converter needed) or it talks SPI or I2C . These three are supported in the hardware of the arduino. However for these and other protocols there also exist software libraries like softI2C, or Dallas oneWire.
So in short most sensors will connect to Arduino but you need to get the voltages right and the protocol right. Then yo can talk to the sensors in the software code.
So in answer to your questions:
1: yes
2: possibly, in theory for every sensor one can design a circuit that let it talk to Arduino, in practice there are limits like budget and common sense 
3: million reasons, sensors existed before Arduino, made for special market (car's using 12V), etc