Are all jenga blocks of exactly same size?
I do not believe that the block dimensions vary much, except because of manufacturing error. The Wikipedia page states that the blocks are:


  Each block is three times as long as its width, and one fifth as thick as its length 1.5×2.5×7.5 cm (0.59×0.98×3.0 in).


And the official website states:


  A classic Jenga game consists of 54 precision-crafted, specially finished hard wood blocks.


I disagree with your assertion that, "blocks dimensions vary, otherwise the occurrence of loose blocks would be symmetric/regular when the tower initially built." If the dimensions were the same, but the weight varied, the weight would not be evenly distributed throughout the tower. That aside, you are probably correct that the blocks are not all exactly the same size.

Only one size block is manufactured, but because machines that cut the wood have certain tolerances (probably in 10s or 100s of microns), you cannot get a perfect cut. Even if you could, the wood surface isn't flat anyway. The ridges of the grain are very deep, as can be seen in this scanning electron microscope images. Finishing the wood would make some of these differences disappear, but even that wouldn't be perfect.