הלכה על חולין 209:2

If someone is about to say birkat ha-mazon, he is required to wash his hands first, and then say the blessing “al rehitzat yada’im;” this washing is an obligation. And so they said, “Mayim rishonim is a mitzvah, mayim ahronim an obligation (hovah), washing during the meal optional.”¹⁶⁶B. Hullin 105a. An obligation – hovah – is a stronger requirement than a mitzvah. And when they said “during the meal,” they meant it is optional between one cooked dish and another. But between a cooked dish and cheese, it is an obligation.¹⁶⁷Ibid., 105b.

One who eats meat, even of a wild animal or fowl, does not eat cheese afterwards until he waits six hours. Even if he waits that period, if he has meat between his teeth he has to remove it. One who chews food for a child has to wait. If afterwards he finds meat between his teeth and removes it, he has to wipe his mouth out before eating cheese (Ran chapter 25). There are those that say that he doesn't have to wait six hours, but rather immediately if he finishes the meal and says the concluding blessing, it is permissible after wiping and rinsing his mouth (Tosafot Hullin 105a - "At the next meal", Mordechai chapter 25, Haga'ot Ashri, Haga'ot Maimoniot chapter 9 of forbidden foods, and Ravya). The simple custom in our countries is to wait after eating meat one hour and to eat cheese afterwards, but you have to say the concluding blessing after the meat (HaAruch, Haga'ot Shaarei Dura) because then it's like a new meal and permissible to eat according to the lenient view. But with no blessing, waiting alone does not good. It doesn't matter if you waited before the blessing or afterwards (his own reasoning, from the Mahari, as opposed to the Issur v'Heter). If he finds meat between his teeth after the hour, he has to pull it out (his own reasoning, from the Ran above). And there are those that say not to say the concluding blessing in order to eat cheese (Aruch in the name of Maharach) but we're not careful about this. And some are careful to wait six hours after eating meat before eating cheese, and it's proper to do so.

Final waters (to wash hands at the end of the meal) are an obligation. And it needs to be cold water and that if fall into a vessel or into anything that separates between it and the ground, such as shavings and that which is similar to them. And one who did not eat anything [messy] and did not touch salt during the meal does not require it.