What is a realistic timeline to increase a website's domain authority by 20 points?
Years. Domain authority uses a logarithmic scale like the Richter scale used to measure earthquakes. Every notch you move up the rung takes exponentially more time, discipline, creativity, outreach, and energy.
If you're asking the question b/c you have to set expectations with someone, I'm with Gaston and would suggest you set business goals and a realistic timeline to reach them versus relying on a metric that correlates with high rankings. Think leads and downloads. If it's an e-commerce site, think sales. Things that are easier to measure and explain to the business.
What are the most important factors to increase a website's domain authority?
Someone from Moz would have to answer that. Here is the page on their site that best explains it. My understanding is the domain authority metric tries to mirror Google's interpretation of a website's importance and would expect incoming links and their sources to be given considerable weight in the calculation.