> Is genetic purging based on random shuffling of the genes of an individual or is it more intentional way of removing deleterious recessive alleles?
There is no intention in evolution. Purging refer to the action of selection at removing deleterious alleles. This term is specifically used when a population goes through a demographic change under which purifying selection becomes more efficient (such as an increase in inbreeding coefficient).
> Do the individuals/couple with deleterious alleles that breed together, pass down the purged genes EACH AND EVERY TIME they produce offspring? Does it happen every time they mate or just some times?
Purging is a population-level process so your second question does not make much sense
Rephrasing the above a bit differently, purging refers to the reduction in frequency of deleterious alleles in the populations. Individuals will transmit whatever allele they can transmit.