Under a franchise arrangement, a person or company purchases the ability to run a local business under a larger company's brand. Depending on the franchise arrangement, the local party may have to meet certain standards established by the larger company and purchase products from the larger company as well.
Half-cock is when the position of the hammer is partially but not completely cocked.
A modified lockdown could mean anything from they're not shackled when they come out of their cell to shower or to be interviewed because of some incident, or they can come out but only in their block, or maybe just a certain wing of that block can come out or maybe kitchen workers can go to work, etc.