How are neurons / synapses "biased"?
The term that most scientists use to describe a synapse's "bias" is synaptic strength. The strengths of synapses depend on their "history".  The change of synaptic strength is called synaptic plasticity. This topic is closely related to memory formation and is a very broad question to answer (groups of wikipedia/scholarpedia pages and tons of reviews, not single publications).

Generally, the strength of a synapse, i.e. the size of the effect of a presynaptic stimulus on the postsynaptic neuron depends on presynaptic and postsynaptic factors. To name just a few:


the number of vesicles released from the terminal,
the expression levels of the neurotransmitter reuptake and/or breakdown enzymes,
the expression level, location and posttranslational modifications of postsynaptic receptors and
uncountable other factors.


Although there have been decades research and a nobel prize (to Eric Kandel) on the topic, there is still a lot to find out.

For a start, you might want to look up 
Synaptic plasticity and/or 
Spike-timing dependent plasticity (long term potentiation and long term depression).

LTP is also a good example to answer all three of your questions (if I understood them correctly).


third question: yes.
second question: LTP (and other mechanisms).
first question: Different frequencies of spike trains are more or less effective at triggering LTP, making them more or less powerful to the change in synaptic strength, affecting the response of future input to the same synapse.