Firth's regression with many fixed effects I've got a sample (n=7000) with a binary dependent variable with many 0s and only a few 1s (150 total) and therefore want to run a Firth's biased reduced regression to estimate the probability of the 1s. So far so good, but my explanatory variables are fixed effects for the individuals (=their individual names). Each individual has between 2 and 50 cases in the data, and all in all there are about 120 individuals. An individual's covariate values can change from trial to trial. As I want to include the individuals as fixed effects I convert them as Dummies. Running Firth's regression with the R logistf package produces several errors now, because of the big number of 'IndividualDummies'. Is there a way to include a big amount of dummies in another way like (1|Individual) in glmer package? Would be great to make it more handy for Firth's regression.

I am not aware of any generalization of the Firth's penalized likelihood approach to mixed effect models (i.e. not clear how one ought to penalize the hierarchical scale parameter in this setting).
However, note that Firth's penalized likelihood approach is basically a Bayesian maximum a-posteriori approach using Jeffreys prior. Thus, one thing you could do is to use software that's intended for (amongst other things) fitting Bayesian generalized linear mixed effects models. There is a number of convenient R packages like brms (or also rstanarm) that would easily allow you to do something like that using familiar R formula syntax. You'd simply have to decide on appropriate prior distributions, for which you might e.g. choose something rather weakly informative in order to obtain something that's not too different from the Firth approach in simple settings (assuming that is desirable to you).
In general, Bayesian approaches with proper priors are pretty good (i.e. they often have better frequentist operating characteristics for plausible scenarios than competing frequentist methods) at dealing with sparse binary/binomial data, if you set sensible prior distributions.
