Hi Dave!
From what has been said so far, I agree with those who think that the lathe bed is twisted. If so, it will NEVER turn parallel.
If you want to turn using the Topslide, you need to set it parallel to an alignment bar using a DTI in the Toolpost, ONCE the bed is free of twist.
On my lathe having done this, I made up and fitted a dowel to ensure that was reset to parallel after any off setting.
You need to borrow a precision level, and check the level at Headstock and Tailstock ends of the bed
If the lathe has a vee bed, you need to mount the level on the cross slide.
Adjust the Headstock end, by shimming the lathe foot, or adjusting the holding down bolts (If it is direct onto a wooden bench, I would lift it up and put a sheet of at least 3mm steel under it, drilled for the holding down bolts to pass through, before trying to set it level and free of twist.
Having set the Headstock end level, across the bed, move to the Tailstock end, and adjust/shim until that end is level.
Then move back to the Headstock end and recheck,/ reset that level, and then move to the tailstock end and reset that level again.
Hopefully, each time the error will decrease. You keep on doing this until the error is either JUST acceptable or even better, Zero.
Try to be consistent about the torque applied to the holding down bolts/nuts, this can affect the readings. It did on my Myford 7 even when mounted on a steel bench on a steel sheet. The slightest tweak on a bolt would send the bubble flying around!
On one Industrial Lathe, the adjusting screws on the heavy cast iron base could not bring it completely level, and I had to resort to shimming between the Tailstock end of the lathe and the base to get the bed free of twist!
If you then want to check the alignment of the Headstock to the bedways, you need mount either an alignment bar or a piece of ground stock, (silver steel?) circa 1 inch/25mm diameter in the chuck.
The bar MUST be consistent in diameter along its length.
Mount a DTI on the toolpost, with the stylus at centre height, and set it to Zero at the Headstock end.
Without touching anything, traverse the saddle to the tailstock end of the bar. If all is well, the DTI will still read Zero.
If it doesn't the axis of the bar is not parallel to the bedways. This could be that for a number of reasons.
1) The chuck may not be mounted square to the axis.
a)Check that all the mating faces for the Backplate and the mandrel are all clean, and free of damage.
b) Check that the mating faces of the Backplate and Chuck are clean and free of damage.
If a) and b) check out as damage free, and the alignment is is still out;
(Hopefully, the rear mating face of the chuck is square to the work holding faces of the jaws, or vice versa.
If not the problems with the chuck need to be sorted out)
2) Remove the chuck from the Backplate, refit the Backplate to the mandrel and lightly skim the surface of the Backplate, just enough to clean it up. (This presumes that the gibstrips on the Saddle and Crosslide are correctly set, and do not allow either to move about when pulled or pushed across their ways).
Refit the chuck and recheck the alignment. Hopefully things will now be fine.
3) If the misalignment persists, then the Headstock mandrel axis would seem to be out of parallel to that of the bedways.
If the lathe is new, you have EVERY reason to complain to the supplier and demand a replacement, or at least to have your machine rectified at their expense, since it is not of adequate quality. You may not have bought a Toolroom lathe, so do not expect a tenth of a thou accuracy, but the figures that you are quoting say that something is radically wrong. You have every right to expect it to be within a thou from Head to Tail.
This too loo long for one post, so more follows.
Howard