Anota a data na tua agenda para não esqueceres.

Anota is the 2nd person singular informal affirmative imperative (tu). In Portuguese the affirmative imperative for tu is formed by taking the present indicative anotas and dropping the final -s, which gives anota.
Anote would be the 3rd person (formal você) imperative.

1. na is the contraction of em + a (feminine a agenda), so em a tua agenda → na tua agenda.
2. With possessive pronouns before most nouns you normally include the definite article (a tua casa, o teu carro). Only with close family members can you drop it (e.g. minha mãe, teu pai).

tua is the informal 2nd person singular possessive, matching tu.
sua is 3rd person or formal 2nd person (quando usamos você).
If you addressed someone as você in Portugal or Brazil, you would say:
Anote a data na sua agenda para não esquecer.

After para indicating purpose, Portuguese normally uses an infinitive. Here it’s the personal infinitive esqueceres, which already carries the subject tu.
If you prefer a finite clause you must add que and the subjunctive:
para que não te esqueças.

Since a data has just been mentioned, it’s clear what you must not forget. You can repeat it (no error):
Anota a data na tua agenda para não esqueceres a data,
but native speakers often drop the repeated object for brevity.

In Portuguese agenda is a diary or planner where you write appointments and dates.
In English agenda usually means the list of topics to be discussed at a meeting.

Yes. You could use:
• apontar (more casual) – “Aponta a data na tua agenda.”
• registar (more formal) – “Regista a data na tua agenda.”

Yes. Both orders are grammatically correct.
• Anota a data na tua agenda (focus on what to note)
• Anota na tua agenda a data (focus on where to note)

It’s optional.
• Without comma: “Anota a data na tua agenda para não esqueceres.”
• With comma for a slight pause: “Anota a data na tua agenda, para não esqueceres.”

You could use the formal imperative or a more impersonal construction:
• “Anote a data na sua agenda para não esquecer.”
• “Registe a data na sua agenda de modo a não a esquecer.”