Я не нашёл подсказку, не говоря уже о тайнике.

This is a question of aspect.

• найти → нашёл = perfective
• находить → находил = imperfective

In this sentence, нашёл is used because the speaker is talking about the result of a search: the result was that nothing was found.

So Я не нашёл... means something like:

• I searched, and in the end I didn’t find it.

If you said Я не находил..., it would usually sound different:

• I wasn’t finding it
• I didn’t use to find it
• I did not find it on some occasion, with more focus on the process or repeated experience

In English, both can sometimes be translated as didn’t find, but in Russian the aspect choice is important.

Yes. In the Russian past tense, the verb agrees with the subject in gender and number if the subject is singular.

Here the subject is я, but Russian past tense still shows whether the speaker is male or female:

• Я не нашёл = a male speaker
• Я не нашла = a female speaker
• Мы не нашли = plural

So нашёл tells you the speaker is masculine.

Because it is the direct object of нашёл.

The dictionary form is подсказка.
Here it is singular accusative:

• nominative: подсказка
• accusative: подсказку

Russian changes noun endings depending on their role in the sentence. Since подсказка is the thing the speaker did not find, it appears in the accusative.

Good question. After negation, Russian can sometimes use either accusative or genitive, and the choice can be subtle.

Both of these are possible in many contexts:

• не нашёл подсказку
• не нашёл подсказки

A rough tendency is:

• accusative: the object is treated as more specific, concrete, expected
• genitive: the object can sound more indefinite, or the sentence focuses more on the absence of the object

So не нашёл подсказку suggests a specific clue the speaker was looking for.
не нашёл подсказки can sound a bit more like found no clue at all.

In modern Russian, accusative after negation is quite common, especially when the object is specific. Still, many native speakers might also naturally say не нашёл подсказки here.

It is a very common expression meaning:

• let alone
• much less
• not to mention

It introduces something that is even more unlikely, more difficult, or more extreme than what was just mentioned.

So the logic is:

• I didn’t even find the clue,
• let alone the hiding place.

This expression is best learned as a fixed chunk:

не говоря уже о + prepositional case

Because the preposition о requires the prepositional case.

The noun is:

• dictionary form: тайник

After о, it becomes:

• о тайнике

So in не говоря уже о тайнике, the phrase after о must be in the prepositional case.

More examples:

• о книге
• о городе
• о тайнике

In this expression, уже adds the sense of escalation: not just one thing, but something even more extreme.

So:

• не говоря о can mean something like not speaking of / not mentioning
• не говоря уже о is the stronger, more idiomatic expression meaning let alone

In other words, уже helps turn the phrase into a set expression that marks a stronger comparison:

• if even the smaller thing didn’t happen, the bigger thing certainly didn’t.

Because не говоря уже о... is treated as a parenthetical or inserted phrase commenting on the first clause.

The main statement is:

• Я не нашёл подсказку

Then the speaker adds an extra comment:

• не говоря уже о тайнике

That is why it is separated by a comma.

You can think of it like English punctuation in:

• I didn’t find the clue, let alone the hiding place.

No, Russian word order is fairly flexible, but the version you have is the most neutral.

• Я не нашёл подсказку, не говоря уже о тайнике.
  Neutral statement.

You could also say:

• Подсказку я не нашёл, не говоря уже о тайнике.
  This emphasizes подсказку.

• Я подсказку не нашёл, не говоря уже о тайнике.
  Also possible, with slightly different emphasis.

The expression не говоря уже о тайнике normally stays together as a unit.

In careful writing, yes: нашёл.

But in everyday Russian texts, ё is often written as е, so you may see:

• нашел

Even when it is written with е, it is still pronounced нашёл.

This is common in Russian spelling. Native speakers usually know from context when е is actually pronounced ё.

Yes, very naturally.

You might also hear:

• Я не нашёл даже подсказку, не говоря уже о тайнике.
• Я даже не нашёл подсказки, не говоря уже о тайнике.

Adding даже makes the contrast clearer:

• I didn’t even find the clue, let alone the hiding place.

So the sentence you have is understandable, but in real speech many speakers would use даже to strengthen the first part.