Is it possible to create a batch file that would open a program in a non-default state?
For example I would like to open firefox and the web console tool located in Tools->Web developer in Firefox 28.0
Unless it is supported by the command line or configuration options for a program then no, you cannot simply open a program in a way that is non-default.
What you can do though is to use a keyboard/mouse scripting program such as AutoIt or Autohotkey with which you can run a program then send the relevant key and mouse clicks necessary to get the program into the state that you require.
These two programs might take a little learning to achieve what you are after but then would do what you need.
Autohotkey also has several script writers that you can use to record a series of keyboard and mouse clicks into a script for you, saving you time and effort learning the syntax. A program that I have seen some recommendations for (but not personally used) is Pulover's Macro Creator.