In general, the relation between the three datasets is as follows:
- The simulation model is initiated with a set of boundary and initial conditions, and will on the long-term provide good mean conditions. However, depending on the frequency of data assimilation, the results on short-term time spans can deviate from the observations, due to internal variability of the model. Besides, models aren't perfect and sometimes have biases for some variables.
- In contrast, the satellite data provides observations. These are of course limited by technical aspects, but as indicated by the table in Section 3 of the link you provided, the quality of the precipitation measurements is very good. However, satellites often have a poorer temporal/spatial resolution than models (a satellite can't be everywhere at once and depending on the type, cannot measure at a very high resolution).
- The reanalysis is a combination of the model simulation and the observations, where both sets are merged (via data assimilation) to provide a coherent dataset. This provides a dataset that can be considered 'pseudo-observations' (they are often used as continental-scale or global scale 'observation' datasets in climate studies), but without the poor spatial/temporal resolution of satellite observations. The biases in the reanalyses should be lower than in the original weather simulation, but may still be present.
Concerning the difference between temperature and precipitation: temperature is much easier to correctly simulate than precipitation (e.g. because of the dry/wet-day transition). As such, on a monthly scale, precipitation biases might be already quite large. For more information on precipitation biases, this paper might be relevant: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2010jd014532 (Stephens et al. (2010): The dreary state of precipitation in global models)
In essence, the dataset you want to use should depend on your needs. If spatial/temporal coverage and historical data is the most important, the reanalysis is probably your best choice. If you want to know more about this dataset and its biases, this article is a good starting point: https://hess.copernicus.org/articles/24/2527/2020/ (Tarek et al. (2020): Evaluation of the ERA5 reanalysis as a potential reference dataset for hydrological modelling over North America). Or, if your goal is impact assessment, you might immediately check this one: https://essd.copernicus.org/articles/12/2097/2020/ (Cucchi et al. (2020): WFDE5: bias-adjusted ERA5 reanalysis data for impact studies)