I have noticed at certain points in the game I will unlock new research options like "Branching Story". I understand that you have to have a staff member research them to use them. How are these research options unlocked initially?
It's based on the individual level of each game element. Here are a couple of examples (not in any particular order, as I haven't written down at this point at which level each system is unlocked for research);
The exception to this is the graphical engines, which are unlocked and need to be researched individually without maxing out the previous graphical engine.
The amount of experience you get for each game element per game created is influenced by the positioning of the slider and elements used in a particular game. The experience is given at the end of the development process and you will still get the experience regardless of whether you release or trash the game.