Im not sure I 100% understand the question so sorry if this doesnt hit the mark, but there are generally four major rules I can think of of the top of my head:
- な adjectives (Nouns defining some quality) need to be followed by a な if you want them to modify a Noun. This is always the case.
- Nouns need to be followed by a の if you want them to modify a Noun.
These rules fall under the first example you listed.
- If the Noun is followed by a suffix or an adverb, functions adverbially in itself, or is part of any larger set compound, the の is often omitted.
This is the second example you listed; ごろ is often seen as an adverbial marker acting as a suffix. “Adverbial” similarly how the english word “about/around” functions adverbially.
- There is also the connective form of だ which is な and is seen in phrases like “なの(Particle or Copula)”.
This is the last example you listed.
なの(Particle):
僕のは猫だ (What is mine is the cat (Implying the cat belongs to me))
僕なのは猫だ (What is me is a cat (Implying I am literally of the quality “cat”, hence “な” is used)
なの(Copula) is most commonly なのです/なのだ and is used to emphasize a sentence:
僕は猫だ (I am a cat) (No emphasis)
僕は猫なのだ (It is that I am a cat) (emphasis on the fact)