Yes, but only of the line is vertical. (It would then be written as x = a, where a is a constant. For example, the line x = 8 does not have a y-intercept. All lines in the form y = mx+b will have a y-intercept.)
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If a line has a slope of 0 and y does not equal 0, then yes.
The y-intercept is the point that is on the y-axis or where the line crosses the y-axis. (hence, y-INTERCEPT)
At what point the line intersects the y-intercept, in an equation y=mx+b, b is the y-intercept.
A line with a y-intercept but no x-intercept will be a straight line parallel to the x axis. It will have a slope of zero.
In the equation y = mx + b the slope is m and the y-intercept is b. The slope of the line is how "steep" the line is, and the y-intercept is where it crosses the y axis.