Displaying X axis in 20 minute increments and smoothing chart

I'm not sure if this is what you want. On your original sheet I added a small table in columns AF:AG for a VLOOKUP. I use this intormation in Column Q (Rounded).

The formula in Column Q is: =HOUR(N2)/24+VLOOKUP(MINUTE(N2),$AF$2:$AG$5,2,TRUE)/1440

I separated the hours from the minutes. I look up the rounded value of the minute using the VLOOKUP. With the TRUE option, VLOOKUP looks for the value and if it finds it, returns the specified column. If it does not find it, it goes up to the row before and uses that data. So it creates a step-function.

I divided the hours by 24 and the minutes by 1440 (minutes in a day) and came up with a number that can be expressed as a time.

From here, I was not sure what you wanted to do, so I made a pivot table that averages the values for the 20 minute blocks and charted that. That information is shown on Sheet1.

OK, so I have one more helper column, called show, and this time I applied it to the axis.

I don't know what that thick gray bar is. It might be the tick marks for all those blank items in the show column.

As for the compression of the data, that's because there are fewer data points in those ranges. I can't get the chart to treat the axis as a date axis even when checking date axis. It think this is because the null string "" is not a date.

If it will help:

I think the easy answer to question 1, starting at the OP again, is to use a scatter chart rather than a line chart. The steps I took:
1) Select chart -> change chart type -> Scatter (lines without marker).
2) The "second axis" data series does not have a range for the "x-values" field, so go into the Select Data dialog -> edit the "second axis" data series -> specify column N as the x values for this series.
3) The x axis scale is "off", so select the x axis -> format axis -> put suitable values in for the axis limits and divisions, or select auto for all parameters.
3a) Remember that time in Excel is a fraction of a day. To get 20 minute divisions, compute/convert 20 minutes to fraction of a day (20/60/24=0.0138888888...) and use that value for the desired major/minor unit.

Is that what you are looking for as far as the axis goes?

As for question 2 -- making it less blocky, I don't have a good idea. It probably depends on exactly what you don't like about the "blockiness" and what you are trying to show with the chart and such. I could see charting a well chosen subset of the data. Or apply a smoothing algorithm to the data. Right now, the blockiness is an accurate depiction of the complete data set that you have asked Excel to chart. Smoothing the chart means doing something "inaccurate" with the charted data, and you would need to carefully decide exactly what you want to do.