Apart from nerve cells and muscle cells, what types of cells do not undergo mitosis in adult man?
To answer the numbered questions:


In general, neurons never divide by mitosis. However, I believe you may have unintentionally misphrased your question; there are functional neural stem cells in the adult human brain as well, and these are believed to give rise to new neurons throughout the lifespan of an individual. They have only been found in specific parts of the brain, though, such as the SVZ and the subgranular zone of the hippocampus (Gonzales-Perez 2012; Behnan et al. 2017). It also bears noting that following an external insult (such as DNA damage, oxidative stress, hypoxia), even terminally differentiated neurons can re-enter the cell cycle and go as far as to replicate their DNA, but this tends to result in apoptosis or arrest at the G2/M phase; such aberrant re-entry into the cell cycle is more frequent in brains afflicted by neurodegenerative diseases (Frade &amp; Ovejero-Benito, 2015). In addition, the possibility to induce neurons to proliferate and form cancers has been demonstrated in retinal cells in mice (Ajioka et al. 2007).  
Correct; as with neurons, muscle cells (myocytes) lack the ability to undergo mitosis. But again, I believe what you really want to ask is whether or not muscles maintain a pool of stem cells that can replace lost cells. The answer to this is yes—there are stem cells within skeletal (Wang, Dumont &amp; Rudnicki 2014)  and smooth muscles (Majesky et al. 2011) that proliferate in response to damage. According to some studies there are stem cells in the adult heart as well, although their regenerative capacity appears to be very low (Bergmann et al. 2009). 


If your intention was indeed to ask about which cells are unable to undergo mitosis, then the answer will likely be a very long list, as no terminally differentiated cell type undergoes division under normal circumstances. This would, for example, include all different blood cell types (erythrocytes, megakaryocytes, neutrophils, eosinophils, basophils, B-cells, T-cells, natural killer cells, mast cells, macrophages), most skin cells (e.g. keratinocytes, melanocytes), epithelial cells (such as those that form the intestinal lining) and such. This would likely include most if not all of the cell types listed here that do not have the "(stem cell)" note next to the links (although I did not confirm this by checking the literature on them).

References:


Ajioka, Itsuki, et al. "Differentiated horizontal interneurons clonally expand to form metastatic retinoblastoma in mice." 
Cell 131.2 (2007): 378-390.
Behnan, Jinan, et al. "Identification and characterization of a new
source of adult human neural progenitors." Cell death &amp; disease 8.8
(2017): e2991.
Bergmann, Olaf, et al. "Evidence for cardiomyocyte renewal in
humans." Science 324.5923 (2009): 98-102.
Frade, José M., and María C. Ovejero-Benito. "Neuronal cell cycle: the neuron itself and its circumstances." 
Cell cycle 14.5 (2015): 712-720.
Gonzalez-Perez, Oscar. "Neural stem cells in the adult human brain."
Biological and biomedical reports 2.1 (2012): 59.
Guo, Dayong, and Lynda F. Bonewald. "Advancing our understanding of
osteocyte cell biology." Therapeutic advances in musculoskeletal
disease 1.2 (2009): 87-96.
Majesky, Mark W., et al. "Vascular smooth muscle progenitor cells:
building and repairing blood vessels." Circulation research 108.3
(2011): 365-377.
Wang, Yu Xin, Nicolas A. Dumont, and Michael A. Rudnicki. "Muscle
stem cells at a glance." (2014): 4543-4548.