2) How many steps are necessary, and what are their individual lengths, i.e. tread lengths? (You'll have to build a table since each step will likely have a unique tread length.)

First we determine the sections to be stepped or paved.

Input := 

Bounds = Solve[Path'[x] == -1/3, x]

Output =

{{x -> 68.2587}, {x -> 127.113}}

Utilizing the graph in Problem 1 and the information we just got, it is clear that for x in the interval:

68.2587 < x < 127.113, the path is stepped;
and otherwise, the path is paved.

Input := 

x1 = x /. Bounds[[1]]
x2 = x /. Bounds[[2]]

Output =

68.2587

Output =

127.113

Next, we determine the step lengths.

Input := 

sum = 0; x = x1;
slps = {}; xs = {}; ys = {};
stlens = {}; lensums = {};
While[x < x2,
	{len = -2/(3 Path'[x]),
	 sum = sum + len,
	 AppendTo[slps, Path'[x]],
	 AppendTo[xs, x],
	 AppendTo[ys, Path[x]],
	 AppendTo[stlens, len],
	 AppendTo[lensums, sum],
	 x = x + len}]

Input := 

StepData =
	Table[{slps[[i]], xs[[i]], ys[[i]],
		stlens[[i]], lensums[[i]]},
		{i, 1, Length[xs]}];

Input := 

TableForm[StepData,
	TableHeadings -> {None,
						{"Slope",
						 "x",
						 "y",
						 "Step Length [ft]",
						 "Cumm Length [ft]"}},
	TableAlignments -> Center] 

Output =

     Slope        x         y      Step Length [ft]   Cumm Length [ft]
   -0.333333   68.2587   35.2872          2.                 2.

   -0.337342   70.2587   34.6165       1.97623            3.97623

   -0.341027   72.235    33.9461       1.95488            5.93111

    -0.3444    74.1899   33.2761       1.93573            7.86685

   -0.347475   76.1256   32.6064        1.9186            9.78545

   -0.350262   78.0442   31.937        1.90334            11.6888

   -0.352771   79.9475   31.2679        1.8898            13.5786

   -0.355008   81.8373   30.5991       1.87789            15.4565

   -0.356983   83.7152   29.9306        1.8675             17.324

   -0.358699   85.5827   29.2622       1.85857            19.1826

   -0.360164   87.4413   28.5942       1.85101            21.0336

   -0.36138    89.2923   27.9263       1.84478            22.8783

   -0.362352   91.1371   27.2587       1.83983            24.7182

   -0.363082   92.9769   26.5914       1.83613            26.5543

   -0.363573   94.813    25.9242       1.83365             28.388

   -0.363826   96.6467   25.2573       1.83238            30.2203

   -0.363842   98.4791   24.5906        1.8323            32.0526

   -0.363621   100.311   23.9241       1.83341             33.886

   -0.363163   102.145   23.2578       1.83572            35.7218

   -0.362467   103.981   22.5917       1.83925             37.561

   -0.361531   105.82    21.9259       1.84401             39.405

   -0.360354   107.664   21.2603       1.85003            41.2551

   -0.358932   109.514   20.5949       1.85736            43.1124

   -0.357261   111.371   19.9297       1.86605            44.9785

   -0.355338   113.237   19.2648       1.87615            46.8546

   -0.353156   115.113   18.6001       1.88774            48.7424

   -0.350711   117.001   17.9358        1.9009            50.6433

   -0.347994   118.902   17.2716       1.91574             52.559

   -0.344999   120.818   16.6078       1.93237            54.4914

   -0.341716   122.75    15.9442       1.95094            56.4423

   -0.338133   124.701   15.281        1.97161            58.4139

   -0.334241   126.673   14.6182       1.99457            60.4085

We see from the table that the total of all stair lengths added together is (in feet)

Input := 

StepLength = lensums[[Length[lensums]]]

Output =

60.4085