What are methylated spirits, and why is this solvent miscible with water?
Methylated spirits is mostly ethyl alcohol, which is infinitely miscible with water.
Methylated spirits has a bit of methanol or phenol added to it, so that should you drink it (and some substance abusers do) you will go blind. Nevertheless, metho is to all intents and purposes ethyl alcohol. Now you can try this yourself, but common salt is insoluble in both methyl alcohol and ethyl alcohol, but the solvent is insufficiently water like to allow dissolution of water. (Of course salt is soluble to some extent in water).
Water, of course, is soluble in both ethyl alcohol and methyl alcohol. Higher chain alcohols have limited solubility in water, as the alkyl chain interactions become more important.
Marker inks probably have some solubility in non-polar solvents, xylenes for instance. You should check the solubility of a permanent marker ink yourself. It should be more soluble in ethyl alcohol than methyl alcohol, but you will have to do the experiment.
On the basis of what I have I said, can you account for the known insolubility of methanol in hexanes?