Do local potentials always precede action potential?
I have to admit that I have never thought about if lower potential stimuli can add up. I have done some research though and you are correct. If there is multiple stimuli that don't reach threshold potential it is possible that those sum up. Summation is possible due to stimuli that are directly after another or that are at the same location after another. 

-> Spatial summation

-> Temporal summation

Do all stimuli have the same effects?

No - some inhibit a reaction, some provoke one. 

How do channels react?
Voltage-gated ion channel contain proteins that react to changes in electrical fields .

At first the sodium channels open up when the stimuli reached treshold potential. That causes the sodium ions to rush into the cell, making it more postive. They start to close before the overshoot.

The potassium channels then start to open and repolarize the membrane.

Single shots doesn't have a huge effect on the membrane. 

Na+/K+ ATPase keeps the settings for action potential alive.