I have seen printers with table screws and bed leveling sensor and printers that have only bed leveling sensor (such as Prusa).
So my question is how does the bed levelling work when there is only a sensor, and no adjustment screws? What will happen if I totally remove the table from the printer and then re-assemble it? Will the print fail or what?
Prusa uses 9 marker points in the bed that are sensed with an induction sensor to determine the X, Y and Z position. Any deviation for skewness or bed level is compensated through the software. Please do note that the bed is pretty level to begin with (by design).
This is precisely described here, please check the video.
Note that Marlin Firmware (which is basically what drives the Prusa printers) has skewness compensation implemented. This is implemented in the configuration file, and found under header
Bed Skew Compensation. You basically print a square and measure the diagonals and insert these measurements into the configuration file. Prusa printers do this automatically by using the measurements of the marker points.