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).