Λίθον ἕψεις.
You're boiling a stone.
In other words: you're wasting your time. No matter how long you boil a stone, it stays a stone. You can see this root in "paleolithic," the Old Stone Age.
Ἀλύπως βίου.
Live without grieving.
The word βίου is a verb here, a middle imperative of the contract verb βιόω. Yes, βίου is also the genitive singular of the noun βίος; the two words are from the same root, but they are not the same word. Just like in English, which abounds in homonyms (both homographs and homophones), there are some Greek words which can have the same spelling and pronunciation but which are different words, and you have to figure it out from context. In this context, βίου as noun does not make sense, but βίου as verb does. More about the many different types of homonyms at Wikipedia.
The best thing is water.
The words are from Pindar in his first Olympian ode: "Water is best, and gold like a blazing fire in the night stands out supreme of all lordly wealth," ἄριστον μὲν ὕδωρ, ὁ δὲ χρυσὸς αἰθόμενον πῦρ / ἅτε διαπρέπει νυκτὶ μεγάνορος ἔξοχα πλούτου." Aristotle, who had a great interest in proverbs, discusses this saying in his Rhetoric. From the root of Greek ἄριστο- we get English aristocracy.
Concerning the shadow of a donkey.
This saying is used to describe something worthless, a trifle of no value whatsoever, and certainly nothing worth arguing about. It was a popular ancient Greek saying as the many citations in Erasmus attest. I especially like the citation from Lucian: Πάντες ὡς ἔπος εἰπεῖν περὶ ὄνου σκιᾶς μάχονται οἱ φιλοσοφοῦντες, "All the philosophers are fighting, as the saying goes, about the shadow of a donkey." Erasmus also reports Demosthenes telling the fable about the donkey's shadow, which you can read here: The Ass's Shadow.
Don't grieve at all.
You could also translate this as "Don't grieve over everything" or "over everyone" — but the idea is really not to grieve, and translating it as "Don't grieve at all" saves the trouble of specifying everything (neuter) or everyone (masculine) for Greek παντὶ. Note also the middle imperative: λυποῦ. We have something like that middle sense in English when we say "don't grieve yourself, don't trouble yourself." This is one of the so-called Delphic maxims recorded by Stobaeus.
And to finish up, here's a random proverb and a random LOLCat too:
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