The AD bonus works on any champion that would normally build attack damage items, be that fighters, carries or AD assassins.
Bloodlust gives champions with AD-scaling physical damage dealing abilities the equivalent of spell vamp.
Elixirs are often bought towards the end of long games when builds are all completed and the extra gold continues to accumulate. They can also be bought mid game to give a temporary stat advantage during ganks and teamfights.
Elixirs require level 9 to purchase.
Elixirs are automatically applied when purchased (even while dead) if there are already 6 items in the inventory.
Only one Elixir effect may be active at a time. Activating a new elixir will remove the old effect.
You cannot buy or activate (as in use one from your inventory) an Elixir while dead.