Old English turf, tyrf "slab of soil and grass, sod," also "surface of grassland," from Proto-Germanic *turfa- (source also of Old Norse torf, Danish tørv, Old Frisian turf, Old High German zurba, German Torf), from PIE root *drebh- "to wind, compress" (source also of Sanskrit darbhah "tuft of grass").
Especially "the race course," hence the turf "the profession of racing horses" (1755). French tourbe "turf" is a Germanic loan-word. The Old English plural was identical with the singular, but in Middle English turves sometimes was used. Slang meaning "territory claimed by a gang" is attested from 1953 in Brooklyn, N.Y.; earlier it had a jive talk sense of "the street, the sidewalk" (1930s), which is attested in hobo use from 1899, and before that "the work and venue of a prostitute" (1860). Turf war is recorded from 1962.
"flat stone for paving," c. 1600, ultimately from Old Norse flaga "stone slab," from Proto-Germanic *flago- (from extended form of PIE root *plak- (1) "to be flat"). Earlier in English as "piece cut from turf or sod" (mid-15c.), from Old Norse flag "spot where a piece of turf has been cut out," from flaga.
"piece of turf or sod with the grass growing on it," used for roofing material, etc., 1530s, Scottish, of unknown origin. Also divet, diffat, devot, etc. The golfing sense "slice of turf cut out by the club in playing a stroke" is by 1884.
"small particle, as of dust visible in a ray of sunlight," Old English mot, of unknown origin; perhaps related to Dutch mot "dust from turf, sawdust, grit," Norwegian mutt "speck, mote, splinter, chip." Hence, anything very small. Many references are to Matthew vii.3.