In transcranial stimulation (for example rTMS) neurons are artificially stimulated into firing frequently, which reduces their firing threshold over time.

This renders those neurons more likely to fire more frequently for some time (several months to a year, in the case of rTMS).

This is used to treat problems like executive dysfunction, by increasing activity in the dorsolateral prefrontal cortex. Stimulating other regions helps with other problems.

Specific drugs or mutations to ion channels that change their activation threshold could change firing threshold. In your example, it may depend on the structure of the receptor and how it senses/interacts with the molecules it senses. Mutations or drugs that change the conformation and/or charge of the detection site could change sensitivity

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yes this also happens naturally in the brain. this is the basis of synaptic plasticity, the mechanism by which we learn. i'm gonna make the distinction though that the electrical potential at which the neuron fires does not change, rather it is the number of receptors on the surface of the cell that changes. these receptors modulate the amount of ions that can flow into/out of the cell and that causes a change in the membrane potential of the cell which leads to it firing.

so changing the electrical potential at which the cell fires is not something we can safely change as it alters way too much about how the cell works in general (and depending on how you do it can kill the organism), but manipulating (with drugs, genetic manipulation) the receptors on the cell surface that modulate the ion flow in/out of the cell is safer and more built for tweaking.