So that no one gets confused, are we all clear on what we mean by Right and Left when talking about lathe tools?
A Right Hand tool actually faces, and cuts, towards the chuck when mounted in the toolpost.
A Left Hand has its cutting edge towards the TaIlstock when mounted in the toolpost, ready to cut.
This confused me for a while when I first started machining.
#1 is a Right Hand knife tool, while # 2 is a Left Hand Knife tool.
The 45 degree tools ( 4 and 8 ) could be used for producing a chamfer on the OD of a workpiece, either to help a Die start cutting, to help the workpiece enter a close clearance bore, or to take off a sharp edge, that might result from facing or knurling a workpiece.
# 6 looks to be an external threading tool, with, as you say, no top rake.
#6 could be used to part off small diameter work, or to make a groove for an O ring of suitable size, or an undercut at the end of en external thread.
Whatever tool you use, it is important that the cutting edge is on the centreline. Too low and it will not cut properly. Too high and the tool will rub rather than cut.
If the tool is on the centreline of the work, a facing cut will leave no pip in the middle of the job, and the tool will cut properly..
A useful exercise would be to make a centre height gauge, to aid setting tools to the correct height. There are various ways of doing this, ranging from "trial and error" to measurements to accommodate the slight (we hope slight ) eccentricity always found in a 3 Jaw chuck.
The tool can be brought to the correct height by putting shims under it, so that when clamped firmly in place, it is at centre height. Shims can be made from pieces of tin (Most tins are about 0.010" (0.25 mm ) thick. Soft drinks cans are aluminium which is softer, and can be hammered to make them thinner, but may eventually become even thinner from the clamping loads applied to the tool.
In the interests of rigidity, to reduce the chances of chatter, try to use the minimum of tool overhang.
If it chatters, reducing the speed may help. A tool with a wide cutting face is more prone to chatter when taking a deep cut. Reducing the depth of cut may improve matters.
Hope that this helps, and is not teaching granny to suck eggs.
Howard