I have some hearsay knowledge about the hiring process for W1 positions. I will do my best to answer correctly, but maybe aeismail can chime in later - I think he is currently on such a position.
1) I notice that the application packages do not require inclusion of recommendation letters. In the US, the typical requirement is that the application package includes at least 3 letters. Will the schools require recommendation letters once selected for an interview or the job? Do letters or references play any significant role at all?
If they did not ask, they probably don't need / want them. In central Europe, letters of recommendation are not traditionally asked for. Many institutions are now starting to ask for LoRs as they adapt more of an US system, but it is certainly not that uncommon that they did not want to see letters.
As Dirk points out in the comments: instead of letters, the committee will often ask experts in your field for "comparing reports", however, this is not under your influence. You cannot select said experts, and you will never see the result.
2) Selection: I know this should vary by case, but how many people do they tend to put on their short list?
As you say, it varies by case, but traditionally at least 3. Dirk states that his experience is rather "at most 3", often less. Let's agree on three-ish.
3) Interviews: I get a feeling that the interview process is brief and a lot less tiring than the American system (for a R1: Typically a 3-day campus visit, job talk, endless meetings with professors, deans, grad students, teaching demonstration, etc, etc). What do they focus on in Germany? (I am asking this as I was invited for an interview, but I was not even asked to do a job talk or teaching demonstration) Are there typically multiple rounds of interviews?
This varies a lot. I have once applied for a job where they invited people for an entire week. However, a one-day campus visit with a talk, dinner, and some meetings with core faculty seems usual. Again, Dirk says: "Always a research talk, always a job interview, often a teaching demonstration, seldomly further meetings or campus tours, never a dinner.".
4) Selection committee: That some European departments practically have a one-person decision making body came as a surprise when I first came to Europe. How is the case in Germany? How many people in the department are typically involved in the decision making process?
Again, varies a lot. Formally, the decision is usually a committee decision, but in reality the actual power often lies with a single person (either the dean or the head of the institute / lab that the W1 professor would be assigned to).
5) Final decision: How fast do they move with their final decisions? For example, the job I am considering only has about a four month gap between application deadline and position start date. This is significantly shorter than a typical US-Search where many schools begin examining applications a year before the position start date, and tells me that they should be moving fairly fast with the decision. Any inputs?
I have no idea. My impression was so far that the process does often not move very fast, but I am sure there are exceptions. Dirk says that one should be prepared to wait at least a few months, but I guess that is true for every committee decision.
All that being said, I should warn you that the actual job of a W1-Professor in Germany is not very well-defined. Some are actual independent professors with their own group, own money, and own research agenda, but some are little more than glorified postdocs with very little factual independence. My instinct is that if they do not make a lot of fuss about "your" job during the application phase, the position you applied to may fall into the latter category. You would be well served to ask very concretely what your actual working conditions would be.
