Is it (ab)normal to propose a course to another university as a PhD candidate I'm an external PhD candidate at a university in Germany, meaning that I have neither a post at the university nor funding. I know this isn't ideal, but my question is this:

My research is related to language education, and for my field work I'd like to compare students from a certain Asian country (mine) with German students. I have done the field work in Asia, and now I need to teach a class in at least two German universities to observe the students' attitude first-hand.

Would it be very outlandish to write an email to a department chair at a neighbouring university in order to propose a class in relation to my PhD project? I've checked their program, and the title of my proposed course isn't there. As this is for the sake of my project, I could do it voluntarily, although I'd be very glad if I'm paid. Should I state that as well (at least the first part)?

I have no idea whether an unsolicited application like this is common in academia (particularly in Germany). In any case I don't want to sound desperate or forcing someone's hand. Thank you in advance for your insight.

P.S. My supervisor is taking a sabbatical leave, so he's not around at the university, and I cannot easily ask questions like this.
Yes, I think it is quite abnormal to suggest that a department takes up a course in their program for the purpose of research field work of a PhD student from another university. To me it seems unlikely that they are going to agree to that.

My field is not education research, but I have a hard time imagining that teaching yourself and evaluating something that goes on in a lecture on a higher level goes very well together.

Some points that you may want to consider to increase your chances of getting to do reliable field work:


Maybe it is sufficient to sit in one or two sessions of an appropriate on-going course just as an observer? Find a suitable course, explain your plans to the instructor, and I think you'll have much higher chances of getting this done than getting to teach a course yourself.
If your field work absolutely requires that you are the teacher, then I would propose that you look for a suitable course that already exists, and ask the instructor of that if you'd be allowed to teach one or two sessions in that course. Of course you have to show your qualification to do that, and it may be helpful if your supervisor could actually make or support that request (assuming that he/she is knowledgable in the field you're looking to teach in).