Cuando lleguen los invitados, ya tendremos preparada la mesa y mi madre habrá dejado envuelto cada regalo.

Because cuando is referring to a future event here: when the guests arrive.

In Spanish, when cuando introduces an event that has not happened yet, you normally use the present subjunctive, not the present indicative. So:

• Cuando lleguen los invitados... = When the guests arrive...
• not Cuando llegan... in this future sense

By contrast, cuando llegan would be used for habitual or repeated actions, like:

• Cuando llegan los invitados, siempre abrimos una botella de vino.
  = When the guests arrive, we always open a bottle of wine.

So in your sentence, lleguen is there because the arrival is still in the future.

These two are related, but they do not mean exactly the same thing.

• Prepararemos la mesa = We will prepare the table
• Tendremos preparada la mesa = We will have the table prepared / ready

The structure tener + object + past participle often means to have something in a certain completed state by a given time.

So tendremos preparada la mesa focuses on the result:

• by the time the guests arrive, the table will already be ready

It is very similar to English we will have the table prepared or more naturally we’ll have the table ready.

Because in this construction, preparada works almost like an adjective describing the object la mesa.

• la mesa is feminine singular
• so the participle becomes preparada (also feminine singular)

Compare:

• Tendremos preparado el comedor
• Tendremos preparadas las sillas
• Tendremos preparados los platos

This agreement happens in structures like:

• tener + object + participle
• dejar + object + participle

The participle is not acting like part of a normal perfect tense here. Instead, it describes the state of the thing.

Both are possible, but they emphasize slightly different things.

• habrá envuelto cada regalo = she will have wrapped each gift
• habrá dejado envuelto cada regalo = she will have left each gift wrapped

With dejar + object + participle/adjective, Spanish often emphasizes the resulting state something is left in.

So:

• dejó la puerta cerrada = he left the door closed
• dejó escrito su número = he left his number written down
• habrá dejado envuelto cada regalo = she will have left each gift wrapped

This makes the sentence feel a bit more focused on the gifts being in a wrapped state by that time.

The future perfect is used to talk about something that will already be completed before another future moment.

Here, the reference point is:

• Cuando lleguen los invitados = When the guests arrive

By that moment:

• ya tendremos preparada la mesa
• mi madre habrá dejado envuelto cada regalo

So the future perfect habrá dejado means:

• by then, my mother will already have left each gift wrapped

It is very similar to English will have done.

Because the two actions are being viewed slightly differently.

• tendremos preparada la mesa describes the table’s state at that future moment
• habrá dejado envuelto cada regalo emphasizes that your mother’s action will already have been completed by then

So:

• tendremos preparada = the table will be ready
• habrá dejado envuelto = she will already have left the gifts wrapped

Spanish often mixes these kinds of future expressions naturally when one part focuses on a resulting condition and the other on a completed prior action.

Ya here means something like already, by then, or by that point.

In this sentence:

• ya tendremos preparada la mesa

the idea is that when the guests arrive, the table will already be ready.

So ya reinforces the sense of prior completion. It helps connect the timing:

• guests arrive
• and at that moment, the table is already prepared

It is very common in this kind of sentence.

Both are possible, but they are used differently.

• cada regalo = each gift
• todos los regalos = all the gifts

Cada treats the items individually, one by one. It always goes with a singular noun:

• cada regalo
• cada persona
• cada día

So cada regalo is correct, not cada regalos.

In your sentence, cada regalo highlights each gift separately, even though the overall meaning is plural in English.

Because it agrees with cada regalo, and cada regalo is grammatically singular.

Even though cada regalo refers to multiple items in total, the noun after cada stays singular, so the participle also stays singular:

• cada regalo → singular masculine
• therefore envuelto → singular masculine

If the sentence used a plural noun, then the participle would change:

• todos los regalos → envueltos

So:

• cada regalo envuelto
• but todos los regalos envueltos

Because los invitados is the subject of lleguen, not a direct object.

The personal a is used before a direct object that refers to specific people:

• Veo a los invitados. = I see the guests.

But here:

• los invitados are the ones doing the action lleguen
• so they are the subject
• therefore no a

That is why you have:

• Cuando lleguen los invitados...

not

• Cuando lleguen a los invitados...

Yes, but the order used here is the most natural with these verb patterns.

Spanish commonly uses:

• tener + object + participle
• dejar + object + participle

So:

• tendremos preparada la mesa
• habrá dejado envuelto cada regalo

This puts the object between the verb and the participle’s descriptive effect. It is a very standard pattern.

You may sometimes see other word orders for emphasis, but the version in your sentence is the normal one learners should remember.

In standard Spanish, los invitados can refer to:

• a group of men, or
• a mixed group of men and women

This is the traditional generic use of the masculine plural.

If the group were all women, you would say:

• las invitadas

Depending on style and context, some speakers may prefer alternatives like:

• las personas invitadas

But in ordinary standard Spanish, los invitados is completely normal for a mixed group.