Is it possible to find all cell types in the human body and their respective transcriptomes by analyzing the human genome (and doing no physical experiment)?
If such a thing is possible in principle, how close (or far) are we from achieving it? Is there any active research in this area? And what is the name of this research area?
No.
Cell types are identified by differential gene expression. Every cell has (effectively) the same genome, but different expression patterns give you different functions.
You could attempt to identify cell types from gene products: the transcriptome (RNA) or proteome (protein), though there would be some challenges as cells we typically consider of one "type" do not necessarily have the same transcriptome/proteome at various time points. A neuron, for example, is distinguishable based on recent activity (for example Benito, E., & Barco, A. (2015). The neuronal activity-driven transcriptome. Molecular Neurobiology, 51, 1071-1088.).
"Cellular differentiation" is the general topic of studying how cells become different types.
Note that even if you attempted something like this (and I'm sure someone has, though likely in some narrower field like deciding whether some cell type should actually be considered multiple types), you'd still need to rely on experimental evidence to verify the result. We're nowhere near being able to abandon actual biological systems in studying biology, and I'd argue it's not even something we should be attempting to do.
