Escribe la fecha en la hoja para que no se te olvide.

Yes. Escribe is the informal singular command (the tú imperative) of escribir.

• escribir = to write
• (tú) escribe = write

So Escribe la fecha... means Write the date...

In Spanish, subject pronouns are often omitted, so instead of saying Tú escribe, Spanish normally just says Escribe.

Because escribes is the normal present-tense form meaning you write or you are writing, while escribe here is a command.

Compare:

• Escribes la fecha. = You write the date.
• Escribe la fecha. = Write the date.

Spanish uses different forms for statements and commands.

On its own, escribe can also be the él/ella/usted present form:

• Él escribe = He writes
• Ella escribe = She writes
• Usted escribe = You write

But in this sentence, since it appears at the beginning and is followed by the rest of the instruction, it is clearly being used as a tú command:

• Escribe la fecha... = Write the date...

If it were a formal command to usted, it would be Escriba la fecha...

Spanish often uses the definite article more than English does. So la fecha literally means the date, even where English might sometimes just say date.

In this sentence:

• Escribe la fecha = Write the date

That sounds natural in Spanish. Omitting the article here would sound incomplete or unnatural.

En la hoja means on the sheet of paper or on the page, depending on context.

• en = on / in
• la hoja = the sheet, the page

Here hoja usually means a sheet of paper. So the idea is:

• Write the date on the sheet of paper

Spanish uses en where English often uses on with paper, pages, and surfaces like this.

Because with writing, Spanish normally uses en.

• escribir en la hoja = to write on the sheet/page

Sobre often means on top of in a more physical or spatial sense. It is not the usual choice for writing something on paper.

So:

• Escribe en la hoja = natural
• Escribe sobre la hoja = less natural here, and may sound like write over/on top of the sheet

Para que means so that or in order that.

In this sentence:

• Escribe la fecha en la hoja para que no se te olvide.
• Write the date on the sheet so that you don’t forget it.

It introduces the purpose of the action:

• write the date for the purpose of not forgetting it

Because after para que, Spanish normally uses the subjunctive.

So:

• para que no se te olvide = so that you don’t forget it

Here olvide is the present subjunctive form of olvidar.

This is a very common rule:

• para que + subjunctive

Examples:

• Te lo digo para que entiendas. = I’m telling you so that you understand.
• Escríbelo para que no se te olvide. = Write it down so you don’t forget it.

Because olvidarse algo a alguien is a very common Spanish way to express something slipping someone’s mind.

So:

• No olvides la fecha = Don’t forget the date.
• Para que no se te olvide = So that it doesn’t slip your mind / so that you don’t forget it.

Both are correct, but they are slightly different in feel.

no olvides

This is more direct:

• Don’t forget it

no se te olvide

This sounds more like:

• so it doesn’t get forgotten by you
• so it doesn’t slip your mind

It is extremely common and very natural Spanish.

In this structure, se is part of the verb pattern olvidarse.

Spanish often uses:

• olvidar = to forget
• olvidarse de = to forget / to fail to remember
• olvidársele algo a alguien = for something to slip someone’s mind

In no se te olvide:

• se is part of that pronominal construction
• te shows to you
• the thing being forgotten is understood to be la fecha

So the whole idea is:

• so that the date doesn’t get forgotten by you
• more naturally: so that you don’t forget the date

Te means to you.

In this expression, the person who might forget is marked with an indirect object pronoun:

• se me olvida = I forget / it slips my mind
• se te olvida = you forget / it slips your mind
• se le olvida = he/she/you(formal) forgets

So:

• para que no se te olvide = so that you don’t forget it

The subject is the thing that might be forgotten — here, la fecha.

So grammatically, the sentence is built like this:

• la fecha = the thing
• se te olvide = is forgotten by you / slips your mind

That is why olvide is in the third-person singular form: it agrees with la fecha, which is singular.

You can think of it as:

• para que la fecha no se te olvide

Spanish often leaves that subject understood because it is already clear from the earlier part of the sentence.

Yes. That is what is understood.

Spanish often omits repeated words when the meaning is obvious. Since la fecha has already been mentioned, the sentence does not need to repeat it.

So:

• Escribe la fecha en la hoja para que no se te olvide.

really means:

• Escribe la fecha en la hoja para que la fecha no se te olvide.

But repeating la fecha would sound unnecessary.

Because it is a negative idea:

• para que no se te olvide = so that you don’t forget it

Without no, it would mean the opposite:

• para que se te olvide = so that you forget it

So the no is essential.

Not exactly.

• papel = paper, the material in general
• hoja = a sheet of paper, a page, or a leaf depending on context

In this sentence, la hoja means:

• the sheet of paper or possibly
• the page

So hoja is more specific than papel.

Yes. In Spain, the normal informal plural command would use vosotros:

• Escribid la fecha en la hoja para que no se os olvide.

Changes:

• Escribe → Escribid
• te → os

So:

• singular informal: Escribe ... para que no se te olvide
• plural informal (Spain): Escribid ... para que no se os olvide

Yes, often.

• Escribe la fecha = Write the date
• Apunta la fecha = Write down the date / make a note of the date

Apunta can sound a little more like jot it down or note it down, while escribe is the more basic write.

Both can work depending on context.

Yes, very natural.

It sounds like a normal instruction a teacher, parent, or another person might say:

• Escribe la fecha en la hoja para que no se te olvide.

It is natural because it combines:

• a common command form (Escribe)
• a normal phrase with paper/page (en la hoja)
• a very common everyday forgetting expression (que no se te olvide)

So this is a good sentence to learn from.