1) This depends on 2) combined with pitch of screws, any gearing between motor and screw, and if you're setting up in metric or imperial.

Essentially, most common stepper motors are 200 steps per revolution, so multiply that by your answer to 2) to get your steps per motor revolution. If there is gearing between the motor and screw, you then need to add that into your equation to get number of steps per turn of the screw. You then need to divide the steps per screw turn, by the pitch of your screw to get your steps per unit. Your unit will be either 1mm for metric, or 1 inch for imperial.
i.e. 200 x 8 = 1600 steps per motor rev. I'm going to assume you're motors will be direct connected to the screws, so you still have 1600 steps per screw turn.
Assuming metric and a 4mm pitch screw, you then divide the 1600 by 4mm to get 400 steps per unit.

2) 8 is usually best the compromise. Any more doesn't gain you any accuracy with a stepper system, and less can make things a bit jerky at low speeds, although it may be needed if your step pulse isn't high enough to get reasonable speeds.

3) How fast is your bit of string? Generic guidance is keep upping the figures until things start stalling, then back of a bit to provide some saftey margin.

4) Depends on how many wires the sensors have. 3 or 4 wire, are easily useable provided thier voltage range is useable. 2 wire, bin them and buy new, as they'll be NAMUR output which interfaces will cost you more than new sensors.