Does Homer consider that the entire user load has to be met from the battery, even if there is enough solar energy available? What I mean is if Homer does take into account that a charge regulator allows energy to flow from the PV to the user AND into the battery?

In a PV-battery system, if the PV power is more than sufficient to serve the load, HOMER will charge the battery with the excess.  If the PV power is not sufficient to serve the load, HOMER will discharge the battery to supplement the PV power in order to serve the load. 

Homer does calculate a scaled peak (kW). But this value is often two low compared to real peak loads, thus I have to consider this fact before choosing the genset or the inverter max. power. Is that correct?

HOMER reports the peak hourly average load encountered over the year.  The peak instantaneous load will indeed be higher than that.  You may have to consider that when choosing the generator or the inverter, although most generators can accept some overload, and inverters typically have a surge capacity that significantly exceeds their continuous power capacity. (It's the continuous power capacity that you should specify in HOMER.)

On the issue of peak loads, if you are synthesizing load data from 24-hour profiles and you think the peak hourly average load is too low, you need to increase the daily and hourly noise values.  Those parameters affect how much random variability HOMER adds to the average load profile.  The Help system contains more information on this topic.