Assault Weapons Ban and Regulatory Reform Act of 2018 This bill amends the federal criminal code to make it a crime to knowingly import, sell, manufacture, transfer, or possess a semiautomatic assault weapon (SAW) or large capacity ammunition feeding device (LCAFD), subject to specified exceptions and limitations. The bill permits continued possession, sale, or transfer of a grandfathered SAW, which must be securely stored. A licensed gun dealer must conduct a background check prior to the sale or transfer of a grandfathered SAW between private parties. The bill permits continued possession of, but prohibits sale or transfer of, a grandfathered LCAFD. Newly manufactured LCAFDs must display serial number identification. Newly manufactured SAWs and LCAFDs must display the date of manufacture. The bill amends the NICS Improvement Amendments Act of 2007 to require law enforcement agencies to be notified when a prohibited person attempts to purchase a grandfathered SAW. It also amends the Omnibus Crime Control and Safe Streets Act of 1968 to allow a state or local government to use Edward Byrne Memorial Justice Assistance Grant Program funds to compensate individuals who surrender a SAW or LCAFD under a buy-back program. Finally, the Bureau of Alcohol, Tobacco, Firearms and Explosives must: (1) develop a framework to evaluate and classify firearms based on their ability to be used to injure or kill, and (2) establish a database to track mass shootings and the firearms used in such shootings.