For example if I have a neuron cell that fires when I say the letter 'A' and is located at a specific place in my brain, will another person have that cell at the exact same place and will it fire when he/she says 'A'?
No, unless you are a C. elegans (or have a similarly simple nervous system), and even then maybe not quite.
Wild-type C. elegans has exactly 302 neurons and they are the same neurons in different members of the species. However, even then, learning can change their nervous system so that it isn't exactly identical in two individuals.
Mammals including humans, however, have brains that are much more shaped by experience and learning. Only the general structure is the same, and even that differs somewhat. It has even been shown that different parts of the brain can be different sizes in individuals with different occupations (see Maguire et al., 2000, for example).
Maguire, E. A., Gadian, D. G., Johnsrude, I. S., Good, C. D., Ashburner, J., Frackowiak, R. S., & Frith, C. D. (2000). Navigation-related structural change in the hippocampi of taxi drivers. Proceedings of the National Academy of Sciences, 97(8), 4398-4403.
White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986). The structure of the nervous system of the nematode Caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci, 314(1165), 1-340.