Note for reading the diagram: the vertical axis is planet size. Only the horizontal axis at one particular vertical level is relevant for the main point here.

    1 R🜨 = Earth
    4 R🜨 = Uranus/Neptune.
    9 R🜨 = Saturn
   11 R🜨 = Jupiter
   ?7–13 R🜨 = estimated range of viable brown dwarfs by one source (*)
   ?10-64 R🜨 = estimated range of red dwarfs
  109 R🜨 = Sun

(*) other sources conflict but some have obvious errors. Wikipedia even has different values depending on the unit

That'll take a while. There's currently no way to detect solar system analoges with current technology and the amount of collected data.

Radial velocity requires about two orders of magnitude better detectors, astrometry requires about one order of magnitude more sensitive instruments, transit photometry requires more time, and finally direct imaging isn't currently feasible for G-type stars like our sun.

In any case, other than direct imaging, all methods would require approximately 40 years of data. Here's why: in order to confirm an observation, you'd need to observe at the very least two orbits.

For Venus and Earth that'd be about 2 years of data. For Mars that'd be about 4 years of data and beyond that, we're talking decades:

  ~24 years for a Jupiter analog
  ~60 years for a Saturn analog
  ~168 years for a Uranus analog
  ~330 years for a Neptune analog

So even a more compact Sol-system analog would require at least a couple of decades of data.

About the water question, that's even harder. Now we're talking direct imaging at resolutions that'd require a leap in technology and capabilities. While mass and radius can easily be determined by a combination of techniques and atmospheres can be analysed if transit photometry is possible, surface composition cannot be determined that way.

Though there have been proposals to infer liquid surface water indirectly from atmospheric composition, I remain very sceptical about such approaches. Planetary geology is quite diverse even in our own system. Such inferred results would need to rest on many shaky assumptions that are hard to test and confirm.

The last question is easily answered - once we can reliably detect Earth-sized worlds around G- and K-type stars, we can get reliable statistics going. So far, observation bias limits us to M-dwarfs (a very alien environment compared to our system) and gas/ice giants when it comes to finding planets (the latter are big enough for both radial velocity methods and transit photometry around G-type stars).

We have the data to analyze the probability of a solar system like ours now. The observational limitations can be accounted for, both because we can understand what our solar system would look like at a distance, and there's enough other data from systems that don't match ours to be statistically significant.

The answer is that our solar system is exceedingly improbable. It is a top spinning stably for billions of years at a time, despite the general shape of it wanting to "fall down". It has several special characteristics in the shape of the outer planets that allow it to support what is in fact a very improbable situation with what we call the "terrestrial" planets being able to stay in the liquid-water zone for billions of years at a time. This turns out to be very abnormal.

It is "improbable"; it is not "inexplicable". There are a number of good and interesting computer simulations explaining how our solar system can come about. However, it is definitely unusual.

It turns out that there are indeed a lot of planets in the galaxy, however, the vast, vast majority of planetary systems end up completely unsuitable for life, visible even at the range we are at now. There's a few buckets they fall into, none of which look like our solar system.

The Copernican principle actually died with exoplanet research. It had a good run, but it turns out that, yes, our Solar System is in fact quite improbable and unusual, and the Milky Way is also improbable and unusual, with its very unusually-quiet central black hole not blasting the entire galaxy with life-ending radiation as is the case with almost all known galaxies. In general most of the galaxies in the universe have vastly, vastly more radiation than the Milky Way. We may not be in the center of our solar system, but it turns out the solar system itself is special, and the galaxy we are in is special.