What are the rules that govern neuron behavior? This is what I know so far:

Neurons are nodes with a number called the threshold.

Neurons are connected to other neurons through directed axons.

Axons take the signals produced by neurons and deposit them on other neurons, these signals can be "negative" or "positive".

Once all the signals coming into a particular neuron are added up, if the sum is greater than the threshold, that neuron fires.

My question is: are these all the rules? And do all neurons have the same rules?
My question is: are these all the rules? 


No.

Some things you left out:

Plasticity (change)


Very-short-term synaptic "plasticity" (changes in synaptic strength); at least a few different forms of this (post-tetanic potentiation, short term synaptic depression, synaptic facilitation).
Very-short-term intrinsic "plasticity" (changes in spiking behavior): spiking accommodation, etc.
Medium to long-term synaptic plasticity; several forms of this: classical Long Term Potentiation or Depression, Spike Timing Dependent Potentiation, synaptic underpinnings of habituation and sensitization in, e.g., Aplysia, synaptic scaling.
Medium to long-term plasticity of intrinsic properties, like threshold, input resistance, firing properties.
Metaplasticity (changing the changeability)


Neuromodulation


Co-transmission of classical neurotransmitters with a neuropeptides
Neuromodulation of ionic conductances directly, postsynaptically
Neuromodulation of ionic conductances directly, presynaptically
Neuromodulation via metabotropic receptors and signaling to the nucleus
Why there are dozens of neuromodulators just for controlling a crab's digestion. (ref)


Odds n' Ends


Electrical "synapses" ("gap junctions")
Refractory periods preventing firing even if above threshold
Extrasynaptic and presynaptic receptors
Retrograde transmission
Axonal failures and branch points
Non-traditional innervation (dendro-axonic, dendro-dendritic, autapses, etc.)
Ephatic coupling (ref) (through local electrical fields)
Wiggling dendritic spines
Glial function as a modifier of neuronal function.


And I'm sure I'm leaving out another 20 or so interesting ones. Arguably, everything I've listed here modifies or has causal relevance to the simple set of rules you provided above. And of course, I'm still leaving out an enormous amount of detail of neuroscience (cell types, architecture/circuit diagrams, molecular cascades, cytoskeletal aspects, development, etc.) that have relevance to "the rules" as well.


  And do all neurons have the same rules?


No. Any of the above may vary depending on cell type, part of the nervous system, individual differences, development, species, sex, time of day or other cycles, environmental factors, and possibly other factors.