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This is, so to say, the next part of the question: Nested NIntegrate - NIntegrate::inum: - error

Now I define three functions:

r[x_] := q[x] /. NDSolve[{q'[t] == 0.0001 + (-1 + I*1 + q[t])*q[t], q[0] == 0}, q, 
   {t, 0, 50}][[1]]

beta = 1;

fn[k_, t_?NumericQ] := Exp[8*NIntegrate[r[s]*Exp[2*beta*1] + 8*r[s], {s, t, k}]]

f00[x_, t_, p_] := 
   p*Exp[-8*NIntegrate[r[s]*Exp[2*beta*1] - 8*r[s], {s, t, x}]] + 
   8*Exp[-8*NIntegrate[r[s]*Exp[2*beta*1] - 8*r[s], {s, t, x}]]*
      NIntegrate[Exp[2*beta*1]*fn[y, t], {y, t, x}]

When I evaluate

f00[20, 2, 0.5]

I obtain the error:

NIntegrate::nlim: s = y is not a valid limit of integration.

The difference between the first question is now both limits of the integral in the definition of fn are variables, and I have to evaluate the integral

NIntegrate[Exp[2*beta*1]*fn[y, t], {y, t, x}]

What I can do?

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The only change I needed was

fn[k_?NumericQ,t_?NumericQ] := Exp[8*NIntegrate[r[s]*Exp[2*beta*1] + 8*r[s], {s, t, k}]]

After this change, Mathematica returned no error.

Please note, that your original version already returned the same results although the error message was printed.

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