Hello danishdeshmuk
Sinking means, that when the output transistor is on, the output is low voltage. In the attached pictures you see circuit one which delivers only an output voltage, and circuit two is an open collector where you can directly connect a relais or contactor. If S1 (S2) is open, T1 (T2) is open too. So Vout = Vce goes to low level. After S1 (S2) is closed, the transistors are also closed and no current flows through.
Yes, that's right. Without signal Vout is high and the Relais is off.
Yes, you are right. Without signal Vout is low and the relais is off, but the the contact is close.
PLC modules with DC input is OK. N.O. sensor modules with voltage output can connect directly. If you have open collector output you need a pull up resistor or an input as a source.
Yes, it's right. Look for picture 2 of Sensor N.O. Don't forget the freerunning diode.
Not specially. You don't know, what type of transistor is inside the sensor. Look what I write above, what voltage is at the output.
I hope it helps.
Regards
Rainer