In the absense of writing experience in my target field, how do I find assignments and evaluate them? A while ago I posted a question wondering if a CS major would be accepted into a Political Science MSc programme and it turned out possible. I am starting next October.

My goal is now to get into an interdisciplinary PhD, I have already scoped some and most of my targets ask me to demonstrate my writing competency as part of their application process. I will also have to write research proposals.

I don't have high steem for my writing, as I have not produced many essays in my undergraduate program. The application deadlines are as early as December and a good proposal can take months to write.

What guidance can I follow to start writing? Especially when I have no assignents and I have to be self-driven. Should I aim to write for a specific online outlet? Even then, how can I get feedback so I can improve faster?

I'm not sure this is the right place to ask, but I don't know where else to turn.
The obvious way to get experience along with feedback is to enroll in a formal writing course. But try to find one in which the instructor is amenable to you making suggestions about general areas and topics. But any writing will be better than no writing. 

A second, but riskier way, is to publish a blog somewhere in which you express your thoughts but allow readers to comment and give you feedback. The world is full of trolls, of course, so be prepared for that, including a way to shut them off and/or back out of the whole project. 

Even writing here on this site you get some feedback in the comments.