After re-reading your questions 1 and 2 I think interpolation basically answers them both. You want smooth and stable values for your counters at any time t, and the way to get that is define an interpolation function from (timeseries, absolute time) to value, or recreate a sufficient range of higher resolution timeseries values that can be graphed directly.
Linear interpolation will give you a line chart. Curve-fitting methods will smooth the charts out, but since you are working with counters you can put some constraints on the interpolation.
Since each bucket represents a change over a period of time it represents an area under the curve for the same interval which should match any graphic representation. https://stackoverflow.com/questions/34983360/create-a-piecew... is basically the question of how to interpolate between data points while preserving that area, which might be overkill for your application but is possible.
Linear interpolation will give you a line chart. Curve-fitting methods will smooth the charts out, but since you are working with counters you can put some constraints on the interpolation.
Since each bucket represents a change over a period of time it represents an area under the curve for the same interval which should match any graphic representation. https://stackoverflow.com/questions/34983360/create-a-piecew... is basically the question of how to interpolate between data points while preserving that area, which might be overkill for your application but is possible.