Yes, the slides should move easily without shake, but not too freely.
Seems a bit odd that the top slide should be so stiff.
Possibly the last owner tightened it for some specific purpose of his (I can’t think / dread to think what) and forgot to reset it.
Or lubricated it with grease and that has hardened off! (Use only oil.)
….
“grinding the back of a tool-holder…” EH? I am not clear what is meant here but this suggests a Quick-Change Tool-Post (QCTP) system, which has three basic parts:
1) The body with built-in clamp that you fit on the top-slide, in place of the simple clamp originally fitted.
2) The tool-holder; a block of rectangular channel section fitted with various clamping and adjusting screws, and which clamps to the body. You need a set of these, at least four to start with. You can add more later.
3) The tool itself, either an HSS tool usually of square-section, a carbide-tip shank or the parting-off blade carrier; which is held in one of the tool-holders.
All of these, certainly the better-quality ones, are precision-made to co-operate to give you repeatable, reliable tool-changing. The lowest-cost ones available though “our” suppliers or other recognised retailers, rather than dubious on-line supermarkets, are usually fine for most of our purposes, though the most basic type does have some drawbacks.
I treated my Myford ML7 to a Myford-branded QCTP and find it eminently satisfactory, so please do as we do: buy tools appropriate to the lathe and its fittings. Don’t try to copy bodges seen on t’Net.
I think I have occasionally seen admissions on this site, to having machined the underside – not the rear – of a insert-tool shank to fit a particular QCTP. That though is an exception, carried out properly, on a milling-machine, by an experienced machinist; and to modify the tool shank itself, not the tool-holders.
The most likely reason is having acquired some second-hand tooling, modifying it to suit the machine.
Taking a grinder to any of the working faces on any of those elements, ruins it by removing its whole point!
Others have said don’t do it – I agree – but your post reads as if you’ve already been and gone and done it. Oh dear….
I rarely look at Ewe-Tyoob but notice there are one or two contributors respected by others here; either for model-engineering and related activities directly relevant to us, or large-scale engineering of interest for its own sake. However, you also sometimes see on this forum warnings about bad workshop habits, poor techniques, sometimes dangerous practices, depicted in many videos.