Several points there Dev.
The earth brush is quite short compared to the HT ones - too long and it will be coil-bound against the armature.
The insulator on the pivot post you mention may just be the little pimple that helps retain the blade that goes on top of the thing. Not an insulator, the opening point is earthed anyway.
To check if the bits are all there, see the exploded view attached. Ignore the circuit board - that's a 'me' thing - where it is shown there should be a simple insulator in mica or similar, between the fixed (live) point brass mounting block and the backplate. As well as a fibre top hat insulator that goes through the backplate and through which the centre screw (also live) passes. Both need to be good. As does the third fibre insulator that isolates the small retaining screw for the fixed point block - and the blade spring of the opening point mustn't touch the brass.
Making and breaking continuity with the points assembled on the mag is sometimes hard to see. If the cb is off, you'll see it, but if mounted and the centre screw is in, you won't see much difference between open and closed, about 0.5 or 0.6 ohm, which many meters at that low a resistance don't reliably show.
A basic continuity test of the low tension, primary, winding can be done by measuring from the cb centre screw to the armature spindle, or mag body if it's assembled with the earth brush fitted. That should show you your 0.5 or 0.6 ohm low tension resistance. Primaries very very rarely go wrong unless a wire breaks off inside.
The HT winding should show, round numbers, about 5000 ohms if you measure from the brass section of the slipring (after taking a pick-up off and turning the mag till the segment is visible) and the mag body, armature spindle etc. If there's no continuity there then either the coil has a break in the HT winding or its connection to the slipring is defective. The winding has a 'spike' on the end which just goes into a very tiny hole in the slipring and touches the inside of the brass strip mentioned, to get the energy from coil to plugs via the pick-ups and brushes.
So the primary coil generates its small AC voltage as it rotates, assuming there's a reasonably decent magnetic field. K2Fs are good at retaining magnetism, but if there's no 'flip' every 180° as you turn the thing by hand, not good. When the points open, HT voltage is induced in the secondary winding. The earth for both windings is common, at the condenser end. Both windings plus the condenser are earthed by a 5BA screw into the brass end cheek.
The condenser is the thing that would benefit most from a megga or insulation tester, but it needs to be disconnected to test it. If it's an original it will certainly have deteriorated. Testing capacitance just needs a meter that has that function; testing for leakage involves putting the insulation tester across the two sides (live and earth), choosing your voltage setting and seeing how much it does or doesn't leak as that voltage is applied. A good test would show, say, 2 Giga-ohms at 500v. A vicious test might involve applying your 1000v, but I wouldn't go that far! If you're lucky, an original might show you a few kilo-ohms of 'leak-proof', at 250v. All too often, it'll show nothing or near enough, and its capacitance can't be measured. The voltage rating of any condenser being tested should be respected, in case the internal insulation is damaged by overdoing things. Many of them allegedly 'self-heal' if perforated by unusually high spikes, but there are limits to how much they will withstand.
If you can be bothered you can create the Lucas coil testing set-up explained in those Workshop Instructions - but absent HT continuity I wouldn't bother, although it's handy to have a test rig, obviously.
On the bench, a K series should easily make fat sparks that go 'clack' at the flick of a wrist. Turning steadily at about 130rpm it should make almost all its sparks, with big gaps of 5.5mm. A really good one will do a fair bit better than that (I've seen 100% sparks at 100 rpm now and again); a dying one might need several hundred rpm to do anything, or may do nothing. All depends what is actually up with the thing. A low tension fault or assembly error will kill anything stone dead - but a dying HT side will often do a bit, cold, at certain speeds, maybe!
Good luck as you proceed!