Is the ruling that the white fluid that exits with stool, which has no smell of semen, does not exit in gushes, and is not followed by fatigue, is Wadi (prostatic fluid), correct?

If the fluid exiting the male organ is thick, white, and often emitted after urination, or sometimes before it, then it is most likely "wady." Its ruling is that it is impure (najis), and ablution (wudu) is required after it, not a ritual bath (ghusl). It is not considered incontinence (sils) unless its emission is continuous throughout most or all of the time.