I'm summarizing some points found in the text as well as Mishnah Berurah commentary to O.C. 128:25
If there are only 10 people and they are all Cohanim, all of them duchen and they bless those that are in the field. If there are women & children, they answer to the blessing, but even if there aren't any, all 10 Cohanim will bless because the answering of "Amen" is not an impediment.
If there are more than 10 Cohanim, only the "extras" (I gather this means the "less important" Cohanim) duchen, and the other 10 will respond "Amen".
Regarding the washing procedure, see Mishnah Berurah commentary #25 in the same chapter. He says that ideally a Levi should wash the Cohen's hands, then a first born ("loose translation of "peter rechem") but not a Yisra'el. If none of these requirements are met, the Cohen should wash his own hands.
I'm deducing from this, that the suggestion that the Cohen washes his own hands means under all situations where there is neither a Levi or Bechor, i.e., all Cohanim.