Yes, you can just loop through the individual features and save them like so:
dat <- read_sf ("~/data.shp")
for (i in seq_len (nrow (dat)))
fname <- paste0 ("~/split_", i, ".shp")
write_sf (dat [i, ], fname)
First of all, make sure your data is in a projected coordinate system whose linear unit is "Meter"
In the tree stand polygon's attribute table, use Field Calculator to make a new field with the expression $area - (264 * (4.5/2)^2 * 3.14). Make sure the field type is "Real" or some other numeric type.
This however will not take into ...
Use the SAGA tool Clip raster with polygon. This tool can be found in the Processing Toolbox.
Click the round green arrow button next to the Polygons layer. This button toggles the option to
Iterate over this layer, creating a separate output for every feature in the layer.