What's the net income of a W1/W2 german professor?
The rules for a German professor are quite different than for a typical German employee. The first thing to note is that you will be a Beamter, which is a very special class of government employees. In particular, you are automatically exempted from the public healthcare system, as well as having to make direct payments into the social security system out of your paycheck. Instead, the pension payments are covered by your employer (the government of the Land in which you work), while the Beihilfe system helps to defray part of your insurance costs (the rest of which you pay for through a private insurance contract). In other words: you get billed for your health care; your private insurance reimburses you for 50 percent of your costs, and 30 percent of the costs for other family members. You submit the remainder of the bill to the university, which reimburses the remaining 50 percent (70 percent). 

The net result of this is that you get a much higher percentage of your income as take-home pay relative to a traditional government employee. Your tax status depends on your marital status, so as a W1, you can expect to take home somewhere between 2800 and 3200 euros per month, as reported by the Öffentlicher Dienst website. There are some differences due to cost of living in different states. However, expect to pay about 200 € per month for health care, or more if you have a family.

However, I should also note that just this week came down a new ruling from the German Federal Constitutional Court stating that the salaries for professors hired since 2005 are too low, and need to be adjusted. This has the potential to adjust salaries upwards somewhat—although it is not yet clear by how much. (The state of Hesse, against whom the ruling was made, has until January to adjust its salaries upwards.)

To answer your other questions:


There are no ranks between W1 and W2.
The base salary is nonnegotiable, as it's set by the state government for which you will work; however, you can negotiate some terms of your "package" (support for students and other workers), and you may be able to get some "performance bonuses" negotiated into the contract.
Teaching duties are set by federal law, and are similarly nonnegotiable (although you can negotiate the ability, for instance, to teach in English rather than German)
Bonuses are not available for single people with no children; instead, according to German law, they're actually taxed at a higher rate.
There is no difference in salary based on nationality.