Mi profesora me pidió que cambiara el encabezado y que dejara más espacio entre una columna y otra.

Because they come after pidió que. With verbs of request, desire, advice, command, etc., Spanish normally uses the subjunctive in the following clause.

• pedir que + subjunctive
• Me pidió que cambiara...
• Me pidió que dejara...

Since the main verb pidió is in the past, Spanish usually uses the imperfect subjunctive in the subordinate clause:

• present: Me pide que cambie
• past: Me pidió que cambiara

This is the usual sequence of tenses in Spanish.

If the main verb is in a present or future time frame, Spanish normally uses the present subjunctive:

• Me pide que cambie el encabezado

If the main verb is in a past time frame, Spanish normally uses the imperfect subjunctive:

• Me pidió que cambiara el encabezado

So pidió naturally leads to cambiara and dejara.

Yes. Cambiara/dejara and cambiase/dejase are both correct imperfect subjunctive forms.

In modern everyday Spanish, especially in Spain, the -ara forms are generally more common:

• cambiara
• dejara

The -ase forms are also fully grammatical, but can sound a little more formal or literary depending on context.

Because the sentence has two requested actions:

• que cambiara el encabezado
• que dejara más espacio...

Repeating que is very natural and makes the structure clearer. It shows that both verbs depend on me pidió.

You can also omit the second que:

• Mi profesora me pidió que cambiara el encabezado y dejara más espacio...

That is also correct. Repeating que just makes the sentence a bit more explicit.

Me is the indirect object pronoun, meaning to me.

So:

• Mi profesora pidió... = My teacher requested...
• Mi profesora me pidió... = My teacher asked me / requested of me

In English, ask often does this job without a visible to, so Spanish learners sometimes forget that Spanish marks the person receiving the request with an object pronoun.

Because pedir means to ask for / to request, while preguntar means to ask a question.

Here the teacher is not asking a question. She is requesting that something be changed, so pedir is the right verb:

• Me pidió que cambiara... = She asked/requested that I change...
• Me preguntó... would suggest she asked me a question

Encabezado means header or heading.

In a document, worksheet, table, or layout context, it usually refers to text at the top of a section, page, or column. It is a formatting/layout word, so header is often the best translation.

Dejar does often mean to leave, but in Spanish it is also very natural to use dejar espacio for leave space / allow space / make room.

So:

• dejar más espacio = leave more space

In design, writing, or formatting contexts, this is a very common way to say that there should be a bigger gap.

Because espacio here is being used as an uncountable noun, like space in English.

So Spanish simply says:

• más espacio = more space

No article is needed. Compare:

• Necesito más tiempo
• Hay más agua
• Deja más espacio

Entre una columna y otra literally means between one column and another.

This structure is very common in Spanish when talking about spacing or relations between repeated items. It emphasizes the gap from one item to the next.

• entre columnas = between columns
• entre una columna y otra = between one column and the next / between one column and another

Both can work, but the full expression sounds very natural and a bit more precise here.

Because Spanish is treating the columns as a pair: one column and another.

That is why the singular is used:

• una columna
• otra

It is not talking about all columns as a group, but about the space between any one column and the next one.

After una columna, Spanish commonly uses otra by itself to mean another one:

• una columna y otra

This is a standard pattern. La otra would sound more specific, as if you were contrasting one known column with a particular other known column. Here the general pattern one ... and another is what Spanish wants.

Because in standard modern Spanish, possessive determiners like mi, tu, su, nuestro normally go directly before the noun, without an article:

• mi profesora
• tu libro
• su casa

So mi profesora is the normal form, not la mi profesora.

Because profesora refers to a female teacher. Spanish nouns for people often change form to match gender:

• profesor = male teacher
• profesora = female teacher

So Mi profesora tells you the teacher is a woman.