Can climate models reliably predict meteorological extremes?
Here's one idea to account for meteorological extremes in our climate models, though I'm not sure if it answers your question and am less certain if it qualifies as reliable (open for feedback on that too):

Take a regional climate model which has simulated into the past and the future. We also have a few decades of observed data to compare the same time period of simulated past. The observed data is going to capture the extreme events much better in every way of course. So, in projecting into the future, if we want to maintain those extremes, we can use the change factor (based on averages, e.g. monthly means) from past-simulation==>future-simulation in order to project past-observed==>future-predicted. Those future-predictions will have the extreme events as they came in the past but with the changed magnitude based on the climate model's past versus future simulations. 

This could be applied to meteorological data such as precipitation and other weather variables in order to inform us about the driving weather forces we'll face in future scenarios. In this way our climate models account for meteorological extremes we've observed recently and in the past, which the models may otherwise fall short on.



Otherwise, as folks have explained in comments on the OP, we simply don't have extensive enough observed data that we can rely upon to calibrate these rarer frequency events. I think your last two bullet points sum up our predicament fairly well:


  
  The available measurements are from a 100-200 year observation period (at best);
  We do not have too much data from different climatic conditions (there might be some phenomena which are not (or not adequately) taken into account in current models, we are somehow biased by the observed, prior 100 year conditions.
  


However, here are a few studies and leads you could explore which try to overcome these challenges in modeling extreme event return intervals and Probable Maximum Precipitation. These seem like they might be addressing your last question but hopefully it helps clarify the potential out there.

This one using extreme-value theory: Van Den Brink et al, 2004. Estimating return periods of extreme events from ECMWF seasonal forecast ensembles.


  ...applications to meteorological and hydrological situations are
  always  hampered  by  the  brevity  of  the  available  datasets,
  as  the  required  return  levels  exceed  the  record  lengths  by  a
  factor of 10 to 100. In order to overcome this problem, we u
  se archived data from all past seasonal forecast ensemble
  runs  of  the  European  Centre  for  Medium-Range  Weather  F
  orecasts  (ECMWF)  since  1987  as  input  for  extreme-value
  statistics analysis. We make use of the fact that the seasonal forecast has little seasonal skill for the Netherlands, which
  implies that the ensembles can be regarded as i
  ndependent sets that cumulate to over 1500 years.
  We investigate the hydraulic response in the Netherlands
  to extreme synoptic-scale weather systems by studying the
  extreme-value  distributions  of  sea  storm  surge  levels,  wa
  ves  and  river  discharges.  The  application  is  detailed  in  four
  practical examples originating from coastal protection, ri
  ver flooding protection, and water management problems. The
  long record length of the ECMWF data reduces the uncertainty in the 10
  3
  -year and the 10
  4
  -year return values considerably
  with respect to the results based on observational time ser
  ies. The ECMWF dataset gives the opportunity to explore the
  distribution of events that depend on several kinds of extreme (Van Den Brink et al, 2004).


This one using the growth factor method, or "NERC M5 method", as explained on page 10: Skaugen and Førland, 2011. Future change in extreme precipitation estimated in Norwegian catchments.

And here is a study which sums the methods up pretty well and proposes a new one for further research, which sounds good to me and relatively like what I described in pretty broad, simple terms in the first part of my answer: Dyrrdal, 2012. Estimation of extreme precipitation in Norway and a summary of the state-of-the-art. There's many quote-worthy passages in this one so I think I'll leave it to you to explore. Sections 3, 4, and 5 are what I imagine you're most interested in because they cover, respectively, the state-of-the-art guidelines/methods from the World Meteorological Organization and various nations; a proposed new-and-improved method; and a conclusion summarize the above.