traced: How to save the data and show the sizes of the steps when using Components and Data Structures of NDSolve?

In some applications, it is advantageous to access components of NDSolve.
However, we may also need to observe the step size taken in the numerical integration, as in the Stiffness Detection.
For example:

{ndssdata} = NDSolve`ProcessEquations[{D[u[t, x], t]==
0.1 D[u[t, x], x, x]+ u[t, x] re[u[t, x], X],
you[0, x] == Cos[2 Pi x]you[t, 0] == u[t, 1]}, u, t, {x, 0, 1},
Method -> "StiffnessSwitching"
(*Method[Rule]"ExplicitRungeKutta" *)]tm = 1;
NDSolve`Iterate[ndssdata, {0, tm}]
sol = NDSolve`ProcessSolutions[ndssdata]

My questions:

  1. How to obtain and trace step sizes as used StepDataPlot[] with NDSolve;

  2. How to save Interpolation Function you[t,x] in order to climb and trace with him after using Obtain[...] Y Plot3D[u[t, x] /. Sun...] After closing and reopening MMA.

I tried DumpSave["", sol] Y Obtain["...\"] what it gives me

Get :: noopen: Unable to open … >>
$ Failed

Please leave your comments and thoughts. Thanks for any suggestions and help.