How is circuit topology chosen in analog designs?
How does 1 play out? 

I spend a portion of my time researching circuits. A good engineer is also a good researcher, they know how to find information. There are many sources, books, research papers, manufacturers app notes to look for circuits that have already been built. This gives one an idea of how to build circuits by understanding each component of the design. 

An engineer can take a design and deconstruct it to find out what all the pieces do. 

If I want to build an op amp, then I need to understand how to build amplifiers on a  transistor level and how they affect the input to output range.

If I want to build an RF signal chain, I gather a list of requirements (like input specs, output specs, costs ect), then go find a circuit/design that will do that (if there is one that fits my requirements). 

2) uses paper, excel and circuit simulators like spice to verify the design will fit the requirements.

One example is I am always looking for low noise temperature sensors, thermistors don't cut it anymore, I look around for new technologies, I found one that uses lasers. I contacted the research group, they asked for more money than I had avalible, and that means we stick with thermistors (until that tech gets commercialized)