While photons can in principle form a black hole, the black hole will not be massless. The mass of the black hole will be related to the energy of the photons that went into it by Einstein's famous equation $E = mc^2$.
The black hole will be a regular black hole, and classically it has an infinite lifetime. Once you include Hawking radiation the black hole will have a finite lifetime, but that lifetime will be no different to a black hole formed by the equivalent amount of massive particles.
In General Relativity we usually make no distinction between mass and energy. The mass/energy is described by an object called the stress-energy tensor, and this is usually written as an energy density. To write the tensor we convert mass to energy using $E = mc^2$.
The mass of a black hole is a surprisingly elusive concept. As it happens there has recently been a question on just this subject here. The Schwarzschild metric is actually a vacuum solution i.e. it describes a spacetime that has no matter or energy present. You cannot point to any place and say "aha, here is the mass!". What we normally think of as the mass of the black hole is more precisely the ADM mass, which is a property of the spacetime geometry as a whole.