You can in general count photons when you have a photon-counting measuring device, such as certain types of diodes or photomultiplier tubes. Just to clarify for other readers, what you're asking here is for what sort of states of the photon field can you predict the number of photons to be counted with high accuracy.
The key issue is not whether the expected number of photons is one or something larger. Of course if the expected number is zero, the prediction is easy.
For standard sources the average photon number can be anything, not just an integer, although the count from your measuring device will be an integer.
For special single-photon emitters, which can be made using small electronic devices, the combined output of a collection of these still has a well-defined photon number.
At the opposite limit, devices which produce well-defined electromagnetic fields have large uncertainties in the photon number, approximately the square root of the expected number. The phase of the radiation field doesn't commute with the photon number, so there's an uncertainty relation requiring that they don't both have definite values.
There's no general principle requiring some particular spatial pattern for a single-photon emitter. The simplest sorts of single-photon emitters, say a single atom in an excited state, tend to have some multi-pole pattern, say dipole. There's major uncertainty in where the photon will be found.
A photon cannot split into two photons without interacting with something else. How would it conserve angular momentum? The simplest all-photon scattering processes require two in and two out. For a discussion, see http://www.slac.stanford.edu/th/lectures/warsaw.pdf
P.s. You've sent in many highly sophisticated questions, right at the limit of what we can handle. I'm curious as to what your story is. I halfway expect at some point to get a grade on this test.
(published on 01/16/13)