Neither period is regulated under the FCRA, which other than stupulatihg that promotiional offers cannot show on a consumer's credit report that is made available to others, does not adress the issue of credit reporting of inquiries.
The aribtrary two year period is based on the CRA decision that their customers are not interested in seeing inquiries that are older than 2 years, and their desire to purge millions of items of information from their databases that have litle remaining value.
The arbitrary 1 year period is based on a determination by Fair Isaac that inquries lose their risk predictive value after one year.
As for deletion of inquires, once an inqury has been filled, the cat is out of the bag and cannot be undone.
The CRA must retain record of the inquiry, and the fact that they provided the CR,
Thus, "deletion" of an inquiry is usually something they simply dismiss, unless the consumer shows that the inquiry actually lacked a permissible purpose, and thus their was a violation of FCRA 604.