Heraclitus of Ephesus (flourished circa 500 BCE) is commonly known only for having said that "you cannot step into the same river twice" or even that "you cannot step into the same river even once". The latter statement was uttered not by Heraclitus but by the sophist Cratylus; as quoted in Aristotle's Metaphysics (Book 4, Chapter 5, 1010a13), "Cratylus ... criticized Heraclitus for saying that it is not possible to step into the same river twice -- for he thought not even once". The quote about stepping into the same river twice is from Plato's dialogue Cratylus (echoed in Aristotle) and Plato may have been quoting only Cratylus, who may or may not have been properly characterizing Heraclitus himself. The existing fragments of Heraclitus state only that "different and different waters flow upon those who step into the same rivers" (Fr. 12).
According to my copy of The Presocratic Philosophers by Kirk and Raven, the original Greek is as follows (quite different, I might note, from what you find at the Wikipedia page.):
ποταμοῖσι τοῖσιν αὐτοῖσιν ἐμβαίνουσιν ἕτερα καὶ ἕτερα ὕδατα ἐπιρρεῖ
Did Heraclitus extend that insight to "all things" (as Plato, or Plato quoting Cratylus, would have you believe)? I have my doubts, since if Heraclitus said something so pithy as "you can't step into the same river twice" and applied that analogy to all things, then I figure someone would have quoted the exact text. Furthermore, Heraclitus said "I prefer things of which there is seeing and hearing and perception" (fragment 61). This indicates to me that he valued the evidence of the senses and would not violate that evidence in order to expound a doctrine that flies in the face of the fact that certain things are more stable than others (indeed his statement about rivers can be understood as merely an observation about things that can be seen, in this case the flowing of waters down a channel to the sea). Perhaps he held that seemingly stable things are imperceptibly changing as well (the fragments of his writings yield no evidence one way or the other), but that does not imply that he thought that everything is in constant flux and that there are no stable or semi-stable identities (a position sometimes described as a "Heraclitean view of the universe"). At least, that's how I read the Greek.
As to psychology and ethics, here are fragments 119 and 101 from Heraclitus, which are quite in line with the Greek tradition:
ηθος ανθρωπω δαιμων
("A person's character is their daemon / genius / animating spirit." -- or however you prefer to translate the untranslatable term "daimon".)
And:
εδιζησαμην εμεωυτον
("I sought out myself" or "I sought the meaning of myself" or "I inquired into myself" -- a kind of restatement of the Delphic saying γνωθι σεαυτον or "know thyself".)