To complete your excelent summary:
Words with one syllabe do not take "´" unless there are two words with the same wording, in which case one of them take "´" to make them different. Examples:
fue, voy, yo, ya, de, ... they do not take "´"
tu (your) but tú (you)
te (you / to you) but té (tea)
de (of) but dé (give)
mi (my) but mí (me)
A very common exception to the rule of the "graves":
The weak vowels (i and u when not stressed) form dipthongues when they are next to another weak vowel or to a strong vowel (a, e and o; and i and u when they take "´"). If the sylabe of the dipthongue is the stressed one, then the stress is allways on the strong vowel. And dipthongues belong allways to the same syllabe: ca-liEn-te, ca-miÓn, Auto (the stressed vowel is in capital letters and the dipthongue is underlined, note that "stress" and "´" are not the same thing because every word is stressed somewhere, but only sometimes the stressed vowel takes a "´")
Think for example in the word "corría". It is pronounced "co-rrI-a" The i is stressed, so the stress in in the 2nd syllabe (from the right end). According to the rule, a word that is stressed in the second last syllabe and ends with a vowel, n or s shold not take "´", but in that case the i and the a would form a dipthongue if the i did not take a "´", so the stress would be in the last sylabe, and more preciselly on the strong vowel: co-rriA. In that case it would be an "aguda" word (stressed in the last sylabe) and because it ends in vowel, by the rule it would take a "´": corriá. You can see that the pronunciation changed completely, form co-rrÍ-a to co-rriÁ, so this is not right.
On the other hand, if you left the word without any "´", just "corria" then this should be a two sylabe word with the stress in the second last syllabe (grave), and because it ends in vowel it does not take the "´": cO-rria. Again the pronunciation is wrong.
So one rule must be broken to get the right pronunciation: co- rrI-a. And it is written corría. Now the í (with the "´") is a strong vowel so the dipthongue is broken, so the í and the a do not belong to the same syllabe.
So words stressed in the second last syllabe (graves) but ended in ía, íe, ío, úa, úe, úo, and these same syllabes with an added n or s at the end, take "´" even when they are graves ended in vowel, n or s (so they shouldn't take "´" by the original rule).
It is ussually said wedo this to "break the diphtongue".
ríos, tía, frío, corría, corrían, corrías, acentúo, acentúa, acentúas, acentúan, acentúes, acentúen, ríen.
(this is, at least, what I remember from school)