is there any goodness-of-fit value if I do a binned log-likelihood fit of a histo like the chi2 in chi2-fits?
And can you explain to me the interpretation of the chi2/nof value after such a log-likelihood fit?
Maybe somebody has already raised this question, but I didn’t find the topic…

after a binned log-likelihood fit you can estimate the chi2 from the bins and the fitted function. That is the values that is printed in the statistics box.
Notice, the different behavior for the empty bins, they are excluded from the chi2 fit while are used in the likelihood fit. If you have many empty bins, the chi2 will not then be a meaningful goodnes-of-fit test.

I should clarify that I am trying to map out the log likelihood value as a function of a certain fit parameter. What I was thinking was to fix all parameters and vary the parameter of interest and get the log-likelihood value, but when all the parameters are fixed the return value for MinFcnValue is always 0. Is there a better method to accomplish this?

You should be able to get the likelihood value by fixing all parameters when using the ROOT trunk or the latest version, 5.34.04.
In case of older versions, you might able to get the value if using Minuit2
(call ROOT::Math::MinimizerOptions::setDefaultMinimizer(“Minuit2”) before TH1::Fit)