A she-wolf in Greek is ἡ λύκαινα.
See, for instance, Plutarch's De Fortuna Romanorum, §8:
εἶτα λύκαινα μὲν νεοτόκος σπαργῶσα καὶ πλημμυροῦσα τοὺς μαστοὺς γάλακτι, τῶν σκύμνων ἀπολωλότων, αὐτὴ χρῄζουσα κουφισμοῦ, περιέστειξε τὰ βρέφη καὶ θηλὴν ἐπέσχεν, ὥσπερ ὠδῖνα δευτέραν ἀποτιθεμένη τὴν τοῦ γάλακτος.
There it was that a she-wolf, ...
Smyth's Greek Grammar, paragraph 232, gives a (probably incomplete) list. (Some of these words aren't used in Homer, and one -- νόσος / νοῦσος "illness" -- is spelled differently in Homer's Ionic dialect.) Of this list, ὁδός, νῆσος, and νόσος are the most frequent (I'd guess these are the three exceptions in your Homer textbook).
Feminines. – a. See ...
ἕλκω is thought to be from a root *selk-, which actually has a Latin derivative in sulcus "furrow" (Gk. ὅλκος). As far as I can see there's no regular way to derive laciō from *selk-. (BTW de Vaan argues that laqueus is unrelated to the family of laciō because of the qu.)
You can see the text of Dionesius Thrax' Τέχνη Γραμματική in Wikisource.
Section 14, ΠΕΡΙ ΟΝΟΜΑΤΟΣ says
"Γένη μὲν οὖν εἰσι τρία· ἀρσενικόν, θηλυκόν, οὐδέτερον"
"Πτώσεις ὀνομάτων εἰσὶ πέντε· ὀρθή, γενική, δοτική, αἰτιατική, κλητική."
I don't know if these terms were used in the Classical period, but I believe this is the earliest Grammar of ...
The origin of the town's name is ultimately unclear, and is missing from many dictionaries. The -don is probably a coincidence, though, and we can probably assume it's Pre-Greek or some borrowing from nearby tribes.
Similar words that might give a clue (καλύβη "kalubē", καλυδίλα "kaludila") are classified as Pre-Greek by Beekes (p. 628 for a smattering of ...
Admittedly this isn't Homer, but it might still be useful. A TLG search (surprisingly) comes up with only two relevant sentences, both from Plato:
Theaetetus 204b-c has the numbers up to six in the neuter gender:
ἕν, δύο, τρία, τέτταρα, πέντε, ἕξ
One, two, three, four, five, six
Timaeus 17a counts up to three with the masculine gender:
εἷς, δύο, ...
Yes indeed! There were definitely pre-modern Greek grammarians who described the grammar of their language in Greek; Dionysius Thrax, quoted by Colin Fine, is one of the more reputable ones. These quotes are all from section 14, Peri Onomatos ("About the Noun"); translations are my own.
Γένη μὲν οὖν εἰσι τρία· ἀρσενικόν, θηλυκόν, οὐδέτερον. ἔνιοι δὲ ...
There are three different sorts of nouns to worry about here!
The simplest, and most common, are gendered nouns. These have one form for the masculine, and a different form for the feminine; they're extremely common, since most adjectives work this way, and adjectives can be used freely as nouns. For example, a beautiful man is καλός, while a beautiful ...
ὁ παῖς and ἡ παῖς are nouns, but
ὁ μαθηματικός (ἀνήρ) and ἡ μαθηματική (γυνή) are adjectives for obvious (omitted) nouns. Mathematics was barely a profession then, so my gut says they would skip ἀνήρ as obvious, but perhaps not γυνή; the LSJ dictionary indicates μαθηματική (ἐπιστήμη) may suggest mathematics, alongside the neutral τὰ μαθηματικά (πράγματα). ...
The answer may be in large part morphosyntactic: Greek often uses verbs to express the meanings of English adjectives like "happy" and "sad". Some examples from the Iliad:
4.255 τοὺς δὲ ἰδὼν γήθησεν ... Ἀγαμέμνων "and Agamemnon was happy to see the two of them"
3.111 ὣς ἔφαθ᾽, οἱ δ᾽ ἐχάρησαν Ἀχαιοί τε Τρῶές τε "So he spoke, and the Achaeans and the ...
You certainly have a point. In classical Greek, Xenophon, etc.
εὔθυμος is your "cheerful happy", but in Homer it is only "kind, generous".
ἄθυμος is Xenophon's sad, but Homer's "fainthearted, spiritless", lackadaisical.
If you could find in Homer
ἱλαρός , "cheerful, joyful"
δύσθυμος , "melancholy" in the lyric poets , or
δύσφρων , "sad" in ...
The two alternative forms Ἀθήνηθεν and ἀπὸ Άθηνῶν have been virtually interchangeable, as you may ascertain from a diachronic text search. St Paul used the latter, of course, but would never use the former -- too archaic. The further back you go, the more the former predominates (down to Ἀθήνῃθεν).
That is to say the primary two meanings of ἀπό: