neuroscience - How are neurons / synapses "biased"?

I'm trying to see if I understand this correctly. I've read the question Can the human brain be reduced to a binary system? and one of the answers explains:

While action potentials are usually binary, you should note that synaptic communication between neurons is generally not binary. Most synapses work by neurotransmittors, and this is a chemically mediated graded response that, for example, act on voltage-gated ion channels.

Looking into the graded response article on Wikipedia:

Postsynaptic potentials are changes in the membrane potential of the postsynaptic terminal of a chemical synapse. Postsynaptic potentials are graded potentials, and should not be confused with action potentials although their function is to initiate or inhibit action potentials

Ok, so from what I understand, involving what I learned in this video about action potential, and those two quotes, there can be a "bias" in the synapse process of neurons that make them more or less likely to reach the threshold for action potential when they receive neurotransmitters as the result of the activity from axons connected to their dendrites. Basically, I have the idea that somehow, the synapse area between neural connections becomes trained based on past interactions on whether or not to fire "easily" or be "reluctant" to fire or else fires more powerfully or weakly contributing more or less toward action potential of neurons on the receiving end.

Edit: On second thought, I also recall learning about a mechanism enforcing recharge time between firing, so the neurons are throttled if they fire too rapidly, a mechanism which, (iirc) if defected can cause epilepsy. Really not sure about that, but it would sort of be the opposite of "training" it seems to me.

So I have a few questions surrounding this subject:

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  Are some "actions" or "transmissions" (for lack of the correct terminology, when the neuron fires) more powerful than others, contributing more dramatically to action potentials of neurons receiving neurotransmitters when it fires?

  
  


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  Or if I'm on the wrong track with that question, how does the bias occur / form over time? Is a bias based on short term or long term series of interactions? How many past interactions are significant in the current state of the bias at any given time?

  
  


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  Is there bias at all?