Muscarinic acetylcholine receptors, or mAChRs, are acetylcholine receptors that form G protein-coupled receptor complexes in the cell membranes of certain neurons (Eglen, 2006) and other cells. They play several roles, including acting as the main end-receptor stimulated by acetylcholine released from postganglionic fibers in the parasympathetic nervous system.
Ligands targeting the mAChR that are currently approved for clinical use include non-selective antagonists for the treatment of Parkinson's disease, atropine (to dilate the pupil for medical examinations), scopolamine (used to prevent motion sickness), and ipratropium (used in the treatment of COPD).
With regard to antipsychotics mentioned in the question's image source (Correll, 2008), Olanzapine and clozapine produce robust increases in hippocampal acetylcholine release during acetylcholinesterase inhibition, while other antipsychotics, including thioridazine, have only small effects (Johnson, et al. 2005). Since thioridazine binds with similar high affinities to muscarinic receptors as olanzapine and clozapine, muscarinic autoreceptor blockade was ruled out as a primary mechanism (Shirazi-Southall, et al. 2002). This study compared in vitro binding affinities and functional activities of olanzapine, clozapine, thioridazine, ziprasidone, risperidone, chlorpromazine and scopolamine at muscarinic M2 receptors with their in vivo potencies to increase acetylcholine release in the rat hippocampus.
To your question (how do you prevent insomnia with natural remedies when stopping these medications)
The main thing to consider, especially when talking about stopping antipsychotic medications, is that insomnia can be the least of the problems. As indicated in the image you posted, stopping them can have withdrawal symptoms which include psychotic episodes, anxiety, and Extrapyramidal Symptoms (EPS). Stopping these medications should only be done under the guidance of your doctor.
Stopping other medications
Whatever the medication is you are stopping, if you suffer from insomnia as a withdrawal symptom, you should speak to your doctor who can advise on the best course of action.
Correll, C. U. (2008). Assessing and maximizing the safety and tolerability of antipsychotics used in the treatment of children and adolescents. The Journal of clinical psychiatry, 69, 26-36. pmid: 18533766
Eglen, R. M. (2006). Muscarinic receptor subtypes in neuronal and non-neuronal cholinergic function. Autonomic & Autacoid Pharmacology. 26(3), 219-33. doi: 10.1111/j.1474-8673.2006.00368.x
Johnson, D. E., Nedza, F. M., Spracklin, D. K., Ward, K. M., Schmidt, A. W., Iredale, P. A., ... & Rollema, H. (2005). The role of muscarinic receptor antagonism in antipsychotic-induced hippocampal acetylcholine release. European journal of pharmacology, 506(3), 209-219. doi: 10.1016/j.ejphar.2004.11.015
Shirazi-Southall, S., Rodriguez, D. E., & Nomikos, G. G. (2002). Effects of typical and atypical antipsychotics and receptor selective compounds on acetylcholine efflux in the hippocampus of the rat. Neuropsychopharmacology, 26(5), 583-594. doi: 10.1016/S0893-133X(01)00400-6