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Correct, if you do not specify ground temperatures in your OpenStudio model than you will likely see the following warning in your EnergyPlus error file:

** Warning ** GetHTSurfaceData: Surfaces with interface to Ground found but no "Ground Temperatures" were input.
**   ~~~   ** Found first in surface=SURFACE 183
**   ~~~   ** Defaults, constant throughout the year of (18.0) will be used.

1. Your model is running because EnergyPlus is applying this default of 18$\circ C$. Defining a Site:GroundTemperature:BuildingSurface object for a simulation tells EnergyPlus what values to use instead of this default.

2. Ground heat transfer can be calculated by knowing the average temperature across the outside face of a surface in contact with soil (basement floors, basement walls, slab on grade, etc.). This is the approach used when surfaces have the Outside Boundary Condition input field set to Ground, which then require the Site:GroundTemperature:BuildingSurface and similar objects that define soil-contact temperatures. However, these soil-contact temperatures are preprocessed by other programs outside of EnergyPlus as a first step and then provided as inputs to an EnergyPlus simulation as a second step.

   Another option to calculate ground heat transfer is through Foundation:Kiva:### objects that allow Kiva to preprocess ground heat transfer at a timestep frequency. One key advantage of this approach is that you don't need to run Kiva as a preprocess step -- it is integrated into the EnergyPlus source code and can perform it's calculations during an EnergyPlus simulation. The other key advantage is that Kiva can model non-uniform insulation placements that the other EnergyPlus objects may not be able to model. For more information, you can refer to posts here and here for more details about the Kiva implementation within EnergyPlus.

3. You can address this in your OpenStudio workflow by either manually changing the EnergyPlus IDF it generates or by applying measures to automatically change the model via scripting. Unfortunately, the Building Component Library (BCL) doesn't have measures that you can download for either the site ground temperature or Kiva objects. There are numerous posts here, here, here, and here about using measures to apply site ground temperatures, as well as a post here about using measures to apply Kiva.

   If you believe that this should be a feature of the OpenStudio application, you can make a new issue as a feature request on the Github site managed by the OpenStudio Coalition that is in charge of development for the OpenStudio application as of April 2020.