Which cells produce HCl produced in stomach? Don't these cells get destroyed by HCl?
Since your first question is a quite basic one (the answer is oxyntic cells) and asking two or more questions in the same post is a reason to close ("Avoid asking multiple distinct questions at once"), I'll address only your second question:


  [Why] don't these [oxyntic] cells get destroyed by HCl?


First, it's important to understand that oxyntic cells (from the greek ὀξύς, meaning "sharp" or "acid") do not produce HCl. They actually secrete two separate ions, Cl&minus; and H+ (and, since HCL is a strong acid, one can say that technically there is &mdash; almost &mdash; no HCL in the lumen, because the ions keep dissociated).

You can find this in any physiology book, but there is a good explanation of the steps in Scientific American (2017):


Potassium ions, K+, diffuse passively from the parietal cell into the lumen.
An active transport pump brings K+ back into the parietal cell,
simultaneously secreting H+ from the cell to the lumen. As much K+
returns by this route as leaks in (1).
Chloride ions, Cl&minus;, diffuse passively from the cell to the lumen, and their negative charges balance the positive charges of the secreted H+.
An exchanger on the opposite face of the parietal cell balances this
loss of Cl&minus; by importing Cl&minus; from the blood in exchange for
bicarbonate ions (HCO3&minus;).
Within the cell, water reacts with carbon dioxide (CO2) to form carbonic acid (H2CO3), which dissociates into H+ and HCO3&minus;.


This image from Lodish (2000) summarises it very well:



Of course, the important factor in lowering the pH (and in eventually killing the oxyntic cell) is the H&plus; concentration, not the Cl&minus; one. Regarding that, it's worth mentioning that, despite the H&plus; concentration in the lumen keeps rising, cytoplasmic H&plus; concentration is never as high as the luminal one, because H&plus; is being pumped out of the cell.

Second, why don't the HCl (actually Cl&minus; and H&plus;, as explained above) already present in the lumen destroy the mucosa? The answer is the mucus layer. 

Still according Scientific American (2017):


  HCl in the lumen doesn't digest the mucosa because goblet cells in the mucosa secrete large quantities of protective mucus that line the mucosal surface. Basic electrolytes, such as HCO3&minus;, trapped inside the layer of mucus neutralize any HCl that penetrates the mucus.


By the way, a similar mechanism explains why doesn't the lysosome has its membrane destroyed by the enzymes it contains.

Sources:


Lodish, H. (2000). Molecular cell biology. New York: Scientific American Books.
Scientific American. (2017). Why don't our digestive acids corrode our stomach linings?. [online] Available at: https://www.scientificamerican.com/article/why-dont-our-digestive-ac/ [Accessed 30 Jul. 2017].