I want to know 1) if there is data for biological N fixation in global forests, and 2) if there is estimation of the fraction of biologically fixed N that is used by plants or retained in forest.
Estimado Geshere, no conozco datos para los bosques del mundo, pero sí tengo información sobre la extracción de nitrógeno por componente para las plantaciones de Eucalytus nittens y Pinus radiata. Estos se estimaron en base a la biomasa exportada desde el bosque.
Exportación de nitrógeno y calcio mediante raleo en un rodal de Eucalyptus nitens de 5 años de edad, Chile (scielo.cl)
(1) (PDF) Costos ocultos de la cosecha de árbol completo: el caso de Pinus radiata en Chile (researchgate.net)
I have to agree with Javiera, I think that the global data you are looking for does not exist in an aggregate form but there might be split singularly for each macro-area or continent.
As for your second question, I think there might be some general data related to species, but unfortunately, the quantity of N fixed in a forest depends on too many variables (e.g. tree species, soil type, and depth, grass cover, slope, aspect, etc.). I will suggest you be more specific on the area you want to work in, you may be able to find some pieces of information!
I am fully in agreement with Alberto's opinion. I did a survey in Google scholar and I mainly found that papers mostly dealing with N fixation in tropical forests. There are many valuable works were done in 2020 and 2021 and I hereby attach two best of them may help to answer your question. I recommend you may also take a look at their references.