You do not need home switches or any other switch for that matter.
The simplest way to set a lathe up for CNC is
Your machine wants to be in PART CO-ORDS (BUTTON ON RIGHT HAND SIDE OF THE MANUAL PAGE)
Put the work in the chuck.
Move the tool to the end of the work and take a facing cut across it.
ZERO THE Z AXIS.
Jog the tool a little way down the work and then touch it onto the work.
Measure the thickness of the work using a caliper and PUT 1/2 THE VALUE IN THE X AXIS DRO (Full value if you are in Diameter mode)
To zero the Y axis (tailstock) you can touch the drill on the end of the workpiece and zero.
The lathe is now set and knows where it is. - i.e. X0 is down the centre of the lathe and Z0 is at the outer end of the workpiece.
Your G Code program should be written from these markers. Include in the code the following at the beginning -
G17 G20(if in inches) or G21(if in mm's) G40 G49 G94. This cancels all offsets and sets the machine so it knows what it is working in.
You can check these settings each time you put in a new piece of work - but as you grow more confident you will find that it is possible to repeat without checking everytime (although bear in mind it is still possible for a motor to miss steps from time to time - you certainly need to keep an ear open)
When finished jog the tool away from the work to a convenient position to remove it.
To do another part, do G0 X0 Z0 which puts the tool back where you started, put in a new piece of stock, pull it out to the tool, tighten the chuck and away you go.
I cannot help you with the rest other than to say -
1. Yes - you must accurately set the number of pulses per unit your computer has to put out to the motor drivers - mine for example is 48,000 per inch. You must do this for each axis.
2. You MUST NOT ramp up the speed too high, because the motors will miss steps. If you have a simple system with no feedback like mine, then this is important. My lathe will only traverse at 4 inches per minute without losing steps. (This is a mechanical thing - I am working on it)
3. You must accurately set the backlash, and enable it.
4,. On your drilling with the tailstock - is the motor powerful enough. Drilling is very heavy work (more that tool turning I think). Your motor must be powerful and the feedrate (as set by the F command - not the motor settings) must be low or you will loose steps again.
If you think about drilling manually - a drill bit takes a lot of pressure and only goes in slowly - it is important to get the spindle speed correct for the size of the drill.
(On my milling head, I put too small a motor - the thing worked very well indeed - it would go up and down - and hold the tool in the same position as I milled - but when it came to drilling - it just stopped! - I have now changed it for one at least three times the power.)
Sorry if you know a lot of this - hope it helps.
Persevere - you will get better all the time. You will not get better software than Mach3 (not without paying a great deal of money, anyway) and this is the best forum in the world.