What are the advantages for submitting my paper to demo or doctoral symposium sessions of conferences
My experience is with Computer Science conferences. Some have a multi-day Doctoral Symposium associated with them. The advantage of them is that you get both some experience in presenting your work and some useful feedback on it. The ones I was associated with have a review selection process so you get some feedback at that point and then were run symposium style, not presentation to a large audience. Other students and a few professors would listen to your presentation and try to give you feedback and ideas. 

I don't believe that the symposia published the work of the students. This was pre-doctoral research in progress. The purpose wasn't publication, but advancement. 

While I wasn't the symposium chair at any of these (part of overall committee), one of my close colleagues was the chair at one of them. I only heard of good experiences. Note that they aren't intended for finished/polished work, but for work in progress where additional ideas might be welcomed. 

I'll also note that our doctoral program at the university used the same idea of symposium presentation with our own doctoral students. Once monthly, students would discuss their work with the other students and the advisors of most of them in an all day seminar. Each student would have a bit of time to report on progess and problems. This was very helpful, especially to those who were struggling a bit with the research as the ideas for progress were usually pretty helpful. 

I see no reason that this wouldn't transfer to most other fields. Even when I was a student of mathematics, my professor had a weekly symposium for his own students. A few other faculty would also attend. But this, for the most part, wasn't student presentations, but rather discussions of mutual interest on which the (few) students were currently working.