About 1, remember the accent rule that when a word is accented on the second-to-last syllable, if that syllable contains a long vowel or dipthong and the final syllable contains a short vowel (and also most οι and αι), then the accent must be circumflex (and conversely, if the final syllable contains a long vowel or diphthong, the accent must be acute). So you have things like πολίτης but πολῖται. I believe this rule has no exceptions.
This by the way implies that the only place where there's a possibility of having either the circumflex or acute accent is in the final syllable of the word, and for there, besides contraction, another reason for the circumflex is that in the genitive and dative, if the ending is accented then it takes the circumflex (if it can). I want to say that this is always the case, but I'm too lazy to check right now, but it's certainly true for the 1st and 2nd declensions (βουλῆς, ὁδοῖς) but it seems to be true elsewhere too (γυναικῶν, τινῶν, ἡμῖν). I believe also that the adverb ending -ως always has the circumflex when accented. I wouldn't be surprised if those cover the vast majority of circumflexes.
And for 3, noticing the iota subscript is useful for distinguishing different forms, e.g. you have nom. sing. ἡμέρα, dat. sing. ἡμέρᾳ, nom. plur. ἡμέραι. I think it's relatively rare to see the iota subscript in the root of words (like ῥᾴδιος) so those are hard to remember for me, but since most of them occur in endings, they're easier to learn and helpful in distinguishing words.