Dear Rob,
Step 1: Install and Configure the Plugin
1. Open QGIS
2. Go to Plugins → Manage and Install Plugins
3. Search for "Radiation ToolBox"
Before 3 you also need to enable experimental plugins - there is a checkbox "Show also experimental plugins" in settings
Step 3: Remove Unwanted Points
No, the PDF describes native editing in QGIS, but we use plugin tools for this - there is a scissors and trash icon on the plugin panel:
Step 4: Save the Modified Data
If you need to save in the LOG format - for Safecast API for example, then you need to save the data using the plugin - the floppy disk icon:
Consider creating a spatial index
This has nothing to do with the plugin itself - its a native QGIS feature.
Might have sense only with some merged data - I used to work with points for the whole Fukushima prefecture... But IMHO has no sense for individual measurements.
If you need to remove duplicate points
No sense here - you do not have "duplicate points" in LOG data. Or maybe sometimes when not moving but "duplicate" would mean having exactly the same coordinates...
Jan