You might already know this, but just to be sure, keep in mind that the US and the German system are structured differently. In Germany, Master's and PhD are almost universally distinct, successive programs. I.e after you finish your Bachelor's, you apply for a Master's program, where after two years of coursework (and a small thesis at the end) you get your Master's degree. With that in hand you then apply somewhere for a PhD which will consist of a few years of research and a proper thesis, but generally no coursework.
As a result, applications for a Master's is rather similar to the application for Bachelor's, i.e. acceptance is mostly depending on your grades (in this case those you had in the Bachelor's, which obviously is required to apply) and you are not expected to decide anything about research yet, since there won't be any except for maybe your Master's thesis, which usually is constrained into 6 months, so just a short project, for which you generally only start to contact people maybe a year into the program. So emailing professors directly is a bit unexpected, since it is unclear what you would want of them. If they are not in the admission committee, there is nothing they can do, and if they are, then you are approaching them through the wrong channels, which could be interpreted as trying something improper. In any case, most programs are quite open anyway, i.e. they effectively take any applicant with the right Bachelor's degree (usually determined via a list of courses that need to be in there) above a certain grade average.
In contrast to that, applying for a PhD afterwards is different in the opposite direction. The focus is solely on research, so you are expected to contact a professor. In fact there usually is no program to apply to, instead you directly ask a professor, if they want to take you as a student, the two of you have a small chat about possible topics and then the rest is just the paperwork (Which is sometimes the only point where you need show your Master's degree). Keep in mind that this depends on the amount of funding and other students the professor has though. If it is a professor that knows you from before, this can be an extremely short, informal process.
With regards to funding keep in mind, that while studying is basically free in Germany, that is the rule only for EU-citizens, if you are not, there might be fees for your Masters. They will generally be smaller than in the US though. You also might not be eligible for any living allowance (Bafög) as a German student might be. In contrast to that, as a PhD-student you are usually paid and expected to do some teaching in return. Sociology is however one of those topics notoriously short on funding, so don't expect to much, but beware of any promises in the form of "work for free now and I'll get you a position later". If you can get any kind of scholarship (German, European or possibly even American), try to do so, professors love people who bring their own funding.
Finally, those are the standards, there are many non-standard programs, even some "graduate-schools" which try to incorporate parts of the American system, but they all differ in what parts, so it is impossible to say anything about them, except read their descriptions.
Edit: As mentioned in the comments, during the Master there is also sometimes the possibility of doing some extracurricular paid research as a Hiwi (Student helper). But those positions are often not advertised and sometimes only offered directly to some of the better students in a class, so there is no use in looking for them at the point of admission. However they can be a great stepping stone into a PhD with the professor you are working for.
