Mi tutora me sugirió resumir el texto en tres líneas y consultar el diccionario solo cuando fuera necesario.

Tutora is the feminine form of tutor.

In Spain, tutor / tutora can mean:

• a school or university tutor
• an academic adviser
• a teacher responsible for guiding a student or group

So mi tutora means my tutor or my adviser, specifically a woman.

Me is an indirect object pronoun meaning to me.

So:

• Mi tutora sugirió... = My tutor suggested...
• Mi tutora me sugirió... = My tutor suggested to me... / My tutor advised me...

Spanish often includes this pronoun where English may leave it out.

Because with a conjugated verb, unstressed object pronouns normally go before the verb.

So:

• me sugirió
• te dijo
• nos recomendó

You could also attach pronouns to an infinitive, but here me belongs with the main conjugated verb sugirió, so me sugirió is the natural structure.

Sugirió is the preterite of sugerir in the él/ella/usted form:

• yo sugerí
• tú sugeriste
• él/ella sugirió

It has a written accent on the final -ó because that is how the preterite third-person singular ending is written.

Also, sugerir is a stem-changing verb in some forms:

• present: sugiero
• preterite third person: sugirió

Because after sugirió, the sentence gives the content of the suggestion as actions:

• resumir el texto
• consultar el diccionario

So the structure is basically:

• me sugirió + infinitive
• she suggested to me to...

This is a common and natural structure in Spanish.

Yes. A very common alternative is:

Mi tutora me sugirió que resumiera el texto en tres líneas y consultara el diccionario solo cuando fuera necesario.

Both versions are possible, but there is a slight structural difference:

• me sugirió resumir...
  focuses on the suggested action directly with an infinitive

• me sugirió que resumiera...
  uses a subordinate clause with the subjunctive

Both are correct and natural.

En tres líneas literally means in three lines.

Here en expresses the format or limit:

• resumir el texto en tres líneas = to summarize the text in three lines

This is a normal Spanish way to say how long something should be:

• en una frase
• en dos párrafos
• en pocas palabras

Usually yes, but in context it often just means lines of writing.

So en tres líneas means the summary should be extremely short, roughly fitting into three written lines. In natural English, depending on context, you might translate it as:

• in three lines
• in about three lines
• very briefly

Modern standard Spanish usually writes solo without an accent, even when it means only.

So:

• solo cuando fuera necesario = only when it was necessary

Older usage often preferred sólo with an accent to distinguish it from solo meaning alone, but today the accent is generally unnecessary unless the writer wants to avoid ambiguity.

This is one of the most important grammar points in the sentence.

Fuera is the imperfect subjunctive of ser, and it is used because the speaker is referring to a situation that is not presented as a simple factual event, but as a condition under which the action should happen:

• consult the dictionary only when it was necessary
• more naturally: only when necessary

After verbs of advising, suggesting, recommending, etc., Spanish often uses the subjunctive in clauses that express conditions, purpose, or non-factual situations.

So:

• cuando fuera necesario = whenever it might be necessary / when it should be necessary

If you said cuando era necesario, it would sound more like you are describing a factual repeated circumstance rather than keeping that sense of recommended condition.

Here it is from ser.

The form fuera can come from either verb:

• ser → fuera
• ir → fuera

But in fuera necesario, it has to be ser, because necesario is an adjective, and ser necesario means to be necessary.

So:

• era necesario
• fue necesario
• fuera necesario

Cuando can take either the indicative or the subjunctive, depending on meaning.

Very roughly:

• indicative: when the speaker refers to something factual or known
• subjunctive: when the speaker refers to something expected, conditional, repeated in a non-specific way, or not asserted as fact

In this sentence, solo cuando fuera necesario means something like:

• only when needed
• only if necessary
• whenever it became necessary

That conditional, non-specific idea is why the subjunctive appears.

Yes. Fuera and fuese are both valid imperfect subjunctive forms.

So you could also say:

...solo cuando fuese necesario.

In most contexts, there is no real difference in meaning.
Fuera is often more common in everyday use.

Because both infinitives depend on the same verb sugirió:

• me sugirió resumir el texto...
• y consultar el diccionario...

The pronoun me already applies to the whole suggestion. Spanish does not need to repeat it before the second infinitive.

Yes. In context, sugerir can be translated as:

• suggest
• recommend
• advise

The exact English choice depends on tone and context.
In a sentence about a tutor telling a student what to do, advised me to or suggested that I can both work well.

Because these verbs do not require a preposition before their direct object.

• resumir el texto
• consultar el diccionario

This is different from some Spanish verbs that do need a preposition. Here the pattern is simply:

• verb + direct object

So:

• resumir algo
• consultar algo