the more direct/exact translation to english would be something like "To him there are two or three years." it's kind of interesting how it expresses the underlying idea that age is something that comes to you or happens to you, rather than something you are.

it is a set phrase that has to be memorized. when describing how old somebody is you always use the dative case.

Often when they talk about a state of being, they use dative case. Ему холодно, ему 3 года, ему трудно. But not for Я рад, я счастлив etc. I can't think of any rules to separately the two states where you would use dative or nominative, but I hope this helped a little.

When the numeral+noun happen in the Nominative, the form of the noun pdepends on the last word of the numeral:

• with один (одна, одно) we use Nominative singular. Use одни with plural-only nouns
• with два (две), три, четыре use Genitive singuar.
• with пять, шесть and everything else use Genitive plural

For год (year) the forms you need are год, года, and, surprisingly, лет. At least, with numbers ("tghe counting form"). This is called suppletion: basically, the same way the English verb "go" borrowed "went" from the verb "wend" and made it its past form. In other contexts the Gen.pl of год is still годов.

Now, a few examples:

• один год, двадцать один год, тридцать один год
• два года, три года, четыре года, двадцать три года, сорок четыре года
• пять лет, десять лет, одиннадцать лет, двадцать семь лет, восемнадцать лет, тринадцать лет, сто лет, пятьдесят лет

The grammar used to be less odd in Old East Slavic, which had the dual number. Most Slavic languages lost it in favour of the simple singular/plural distinction, all while replacing missing forms with what they could find. So if the above scheme looks sketchy to you—well, it actually is.

Sounds fine to me.

Not when stating someone's age. Only the dative case can be used.

2,3,4 combine with "года", so "2 or 3" also do. If it were "4 or 5" we would indeed use "четыре или пять лет".

In general, when the "base form" is expected, the last word of the numeral will force the form of the noun:

• 1 → Nom. sg. "один стакан"
• 2, 3 or 4 → Gen.sg. "три стакана"
• 5 and above → Gen.pl. "шесть стаканов"

When counting years, we use the irregular Genitive plural "лет" instead of "годов". Otherwise it works the same as for any other noun.

Oh, and whenever the combination of a numeral and a noun takes up a slot in the sentence that requires some other case (e.g., Dative or Prepositional), the numeral and the noun will take whichever case is required by the sentence. The noun will take the singular form for numerals like 1, 21, 31 etc and the plural form for everything else (e.g. "У нас нет трёх стаканов" or "Строительство заняло более 21 года".)