I can't run your notebook because I don't have the file which is imported. But the error you see, "1 is not a valid variable," is occurring because the fit parameter symbols were previously set to numerical values. For example, Cb0 is used as a fit parameter variable, but was earlier set with Cb0 = 1. The variables given to NonlinearModelFit must not have previously defined values.

Your function Model9, does not evaluate to a solution of the differential equation. E.g.,

Model9[.03, .046, .0666, .05, .1]

returns

Cb[0.1] /. {Derivative[1][Cc][t] == 
   137.344 (0.0378 Cam[t] + 0.0662 Cb[t] + 0.0378 Cbm[t] - 
      0.0028975 Cc[t]), 
  Derivative[1][Ca][t] == 20000. (-0.0229 Ca[t] + 0.0378 Cam[t]), 
  Derivative[1][Cb][t] == 
   925.926 (0.02 - 0.1091 Cb[t] + 0.0378 Cbm[t]), 
  Derivative[1][Cam][t] == 
   2472.19 (0.0229 Ca[t] - 0.0756 Cam[t] + 0.001145 Cc[t]), 
  Derivative[1][Cbm][t] == 
   2472.19 (0.0229 Cb[t] - 0.0756 Cbm[t] + 0.001145 Cc[t]), 
  Cam[0] == 0, Cbm[0] == 0, Cc[0] == 0, Cb[0] == Cb0, Ca[0] == 0}

From your output you can see that Cb0 has a value (it is 1 and is set at the top of your notebook). That is what the error is telling you. The variable that you use to fit cannot have a value.