It's not "υ" before a consonant in general that is pronounced /v/ or /f/ - for example, λύση "solution" is not pronounced "lfsi".
It's the combinations αυ ευ which are pronounced /av~af/ and /ev~ef/ - and that even before a vowel (e.g. δουλεύω /ðulevo/ "I work").
And when two vowel letters together have a certain sound, then the accent goes on the second vowel letter; not only when that "certain sound" is a single sound as in αι οι ει ου, but also with αυ ευ.
If you have two vowel letters and the first one has an accent, then the two vowels are pronounced separately. So for example, ταΐζω /ta.i.zo/ "I feed" has the past tense τάισα /ta.i.sa/ "I fed"; the accent on the first vowel shows you that αι here is two vowels "a+i" rather than a digraph pronounced "e". (And so the diaeresis is not necessary in that form to show that the two are pronounced separately.)
Similarly, πραΰνω "I soothe" would have imperfect πράυνα "I soothed" pronounced /pra.i.na/.
Greek only has one kind of accent, but not only one kind of diacritic :)
The diaeresis is two dots side by side above a letter and it serves the same purpose as in English: to separate two vowels, i.e. to show that two vowel letters next to each other are to be read separately, rather than together representing a single sound.
It's not used as much in modern English, but you used to see such words as naïve, coöperate, Noël. It's also sometimes used to mark otherwise silent letters as pronounced, as in Brontë (Tolkien also used this in some of his Elven names, such as Eärendil or Anairë.)
So in Greek you can have words such as γαϊδούρι "donkey", where the diaeresis (διαλυτικά) shows that the first syllable is /ɣai/ and not /ʝe/.
It's not a terribly frequent diacritic, though.
Sometimes you can have a syllable where the vowels are spoken separately and the second vowel is accented; in this case, you need both the diaeresis and the accent, and then you get ΅ as in αΐ or εΰ.
If the vowels are spoken separately and the first vowel is accented, then you don't need the diaeresis, as the position of the accent makes the pronunciation clear, e.g. άυλος "immaterial" can't have /av/ the way αυλή "yard" does.
I think those two (diaeresis and accent) are the only diacritics used in modern Greek, though; ancient Greek had a few more, such as one to show where two words, the second beginning with a vowel, had been smooshed together.
Now the ευ, αυ, αι, οι, ει... make sense. I know what a diaeresis is. We have it in Spanish: pingüino, agüero, it is used with "güe" and "güi" dipthongs. I could't see the "two points" over ταΐζω.
Γεύμα and άυλος. Now I see the accent goes over the letter α and not over the letter υ.
Ιn ancient Greek the diphthongs (αυ/ευ) were pronounced as /au/eu/, so the υ was pronounced as a vowel back then. Today that the υ is pronounced as a consonants we still mark it with the accute for historical reasons. Greek orthography is one of the most conservative ones you can find :)
Why is the accent on upsilon if it's pronounced as a consonant?
Greek spelling is historical/etymological -- and αυ, ευ used to be diphthongs and were therefore accented on their second letter, and even now that they have become vowel+consonant, the spelling is still the same, with the accent on the second "vowel" of the "diphthong".
If you put the accent on the first, it would indicate that the two vowels belong to separate syllables, and then the upsilon would be pronounced as a vowel, e.g. άυλος (a-i-los) "incorporeal" (from α- "a-, un-, non-" + ύλη "matter, substance, material").