Some of these questions could be answered using common sense, and others are a little more technical. Low-energy building design is becoming increasingly used in both residential and commercial designs and aims to utilize natural heating from the sun, natural airflow, natural lighting and thermal mass among other things, in order to keep running costs down.
Windows can be double-glazed to insulate (both heat entering and leaving a space), tinted and placed in optimum locations to allow for the best lighting and heating of the space.
Entrances can be well insulated and placed at optimum locations to maintain heat within the building.
One measure of air quality is the carbon dioxide level. Obviously, plants use carbon dioxide to make oxygen and can help to increase the oxygen levels in a building. Office building HVAC (Heating, Ventilation and Air Conditioning) systems often have carbon dioxide sensors and can sense when the levels become too high. If levels do become too high, building occupants can feel drowsy (not good for productivity!).
I think thermal inertia is akin to 'thermal mass', in other words the ability of a building material to store and release heat. Concrete is renowned as having a very high thermal mass and is a good insulator. Timber is at the opposite end of the spectrum and thermal insulation is usually used in conjunction with timber-framed buildings. The amount of thermal mass required is dependent on the climate the building is in, and must also be balanced with the natural heating of the space. There are a many success stories and almost as many disaster stories about the use of thermal mass. As long as the design is matched with the natural heating and is specific to the location and climate of the building, it has the potential to be a good design. A mistake that has often been made is copying a building design that worked in one climate, but is completely unsuited to the climate the new building is in. This can result in extreme overheating or under-heating of the building and require renovations or HVAC equipment to be installed.
Windows and even 'natural fans' can be placed in specific locations in order to properly cool and circulate air in a building without the need for powered ventilation. Of course, this will depend on the climate and wind characteristics for the area. Computational fluid dynamics (CFD) is increasingly being used to predict and design the air flow within a building (both powered and natural), and allows a designer to see exactly how the specific building should perform.
The main thing to remember in low-energy building design is that each design is only appropriate for a particular location and climate. There are many ways to achieve the same basic outcome and each different building will always require a custom solution. Some climates will benefit from a large amount of thermal mass (e.g. thick concrete walls), where other buildings will perform well with low thermal mass (such as a light timber design, if solar heating is properly controlled in the design of the building's windows and other open spaces). Making relatively small changes in the design phase can have a huge impact on the thermal performance and life-cycle costs of a building.
