I still can't grasp the idea of SFM. I'm turning 1/2" mild steel at around 450 RPMs and using the leadscrew, taking out around .015
Interesting that you're mostly turning mild steel and dulling HSS. For one thing, you're going too slow for 1/2" mild steel, although there are many kinds of mild steel and you haven't told us what you're using. On average, though, mild steel has a cutting speed of about 100 sfm and for a 1/2" work piece, that gives you an rpm of about 764. A HSS ground well at conventional tool angles will easily go 0.025 to 0.030 per pass in mild steel. A modified HSS tool will easily double that or more, and it will cut for a long time before needing sharpening. So, I suspect that your grind is the issue. If you show us your tool we might be able to help.
Size of your HSS tools does matter. 1/4" tooling will work for most things but a 3/8" tool is stiffer and will cut better if your lathe can handle it.
As for grasping SFM, it's pretty simple. Every material has a particular cutting speed that is given in surface feet per minute, or SFM. You can find a good one on LMS:
https://littlemachineshop.com/reference/cuttingspeeds.php
Look up the cutting speed for the material you're cutting and plug it into this equation: RPM = SFM X 3.82 / D, where SFM is the cutting speed for your material, 3.82 is a constant and D is the diameter of your work piece. Solve for RPM and that is the speed you run your lathe at for that material and work piece. Note that cutting speed varies with the type of tooling you're using, HSS or carbide. Using your stated work piece as an example, the cutting speed for mild steel is about 100 so RPM = 100 X 3.82 / 0.5" = 764 rpm when using a HSS tool. Pretty simple.
Note that this speed is only a recommended starting point. You can adjust this speed and feed as needed. For example, if you tried turning at 750 rpm and encountered chatter, slow the speed to 600 and increase your feed a bit and the chatter should resolve. Again, the calculated rpm is not written in stone.
Cannot comment on your breaking carbide inserts without more info - material, tool holder and insert, cutting conditions, etc. More info will help us help you.