The parting inserts I have bought always have a tip that is parallel with the lathe axis so that they produce a flat-bottomed groove. Inevitably, this means that the work will break off when the remaining material is too weak to support it and almost always leave more or less of a pip. In the days of HSS tools, the parting tool would often be ground at a slight angle on the tip so that the RH corner cut slightly more deeply than the LH corner. Get it right and the work would drop off leaving any pip on the material left in the chuck. However, my own experience was that this slight angle could also cause the tool to go in to the work and progressively move to the right, leaving a concave face on the parted-off work. These days, I use standard inserts and accept that I need a second operation to clean up the face. I believe that inserts with angled tips are available, although I have never gone in search of them.
I cut brass dry, and probably faster than you are, although my own lathe is a bit heavier than a mini-lathe. Main thing is to keep a steady feed but at least the chips tend to fly off and not jam, as they can do with steel.