Mi estus fidinta ŝian konsilon, se mi estus rimarkinta la problemon pli frue.

Because this sentence is about an unreal past situation.

• Mi fidus... usually means I would trust... in a more general, present, or future hypothetical sense.
• Mi estus fidinta... means I would have trusted..., referring to something that did not actually happen in the past.

So the compound form makes the past meaning clear.

-inta is the past active participle ending.

• fidinta = having trusted
• rimarkinta = having noticed

When you combine that with estus, you get a meaning like English would have + past participle:

• estus fidinta = would have trusted
• estus rimarkinta = would have noticed / had noticed

Because both parts describe a counterfactual past situation:

• Mi estus fidinta ŝian konsilon = I would have trusted her advice
• se mi estus rimarkinta la problemon pli frue = if I had noticed the problem earlier

In Esperanto, using estus + -inta in both clauses is a clear way to show that both actions are imagined and already in the past.

Because they are in the accusative, which usually marks the direct object.

• ŝian konsilon is the object of fidinta
• la problemon is the object of rimarkinta

Also, ŝian matches konsilon because adjectives and similar words agree with the noun they modify in both number and case.

So:

• ŝia konsilo = her advice
• ŝian konsilon = her advice, as a direct object

Because ŝian means her, referring to some female person.

Sian is a reflexive possessive and is used when the possessor is the subject of the same clause, typically in the third person.

Here the subject is mi, so sian does not fit. You need ŝian to mean her advice.

Because Esperanto konsilo is a regular countable noun.

So Esperanto can say:

• konsilo = advice / a piece of advice
• ŝian konsilon = her advice / her piece of advice

English treats advice as uncountable, but Esperanto does not have to follow that pattern.

Pli frue means earlier.

It uses frue because it modifies the verb idea rimarkinta:

• frua = early, as an adjective
• frue = early, as an adverb

Here the meaning is noticed earlier, so an adverb is needed.

Because se mi estus rimarkinta la problemon pli frue is a subordinate clause.

Esperanto normally separates subordinate clauses with commas, so the comma before se is standard punctuation here.

Yes. You can also say:

Se mi estus rimarkinta la problemon pli frue, mi estus fidinta ŝian konsilon.

That means the same thing. Esperanto word order is fairly flexible, and putting the se clause first is very common.

Not exactly.

• fidi ŝian konsilon = to trust her advice
• sekvi ŝian konsilon = to follow her advice

In this sentence, fidi emphasizes belief or confidence in the advice. If you wanted to emphasize actually acting on it, sekvi would be more direct.