Si quedan moras, las pondré en el postre.

Because this is a real, open condition: if there are any blackberries left. After si in this kind of sentence, Spanish normally uses the indicative, not the subjunctive.

So:

• Si quedan moras, ... = If there are blackberries left, ...

You would not say si queden here.

A useful pattern is:

• Si + present indicative, future / command / present / etc.
• Si llueve, me quedaré en casa.
• Si tengo tiempo, te llamo.

Here quedar means to remain / to be left.

So quedan moras literally means something like:

• blackberries remain
• there are blackberries left

This is a very common use of quedar in Spanish:

• Queda pan. = There is bread left.
• Quedan dos entradas. = There are two tickets left.

Notice the verb agrees with what remains:

• Queda una mora.
• Quedan moras.

Without an article, moras means blackberries in a general, indefinite sense: any blackberries / some blackberries.

• Si quedan moras = If there are any blackberries left

If you said las moras, it would sound like you are referring to specific blackberries already identified:

• Si quedan las moras... = If the blackberries are still left...

In this sentence, the article is usually omitted because the meaning is simply if there are any left.

Las is the direct object pronoun meaning them, and it refers back to moras.

• moras is plural and feminine
• so the pronoun is las

So:

• las pondré = I will put them

Spanish often uses an object pronoun instead of repeating the noun:

• Si quedan moras, las pondré en el postre.
• literally: If blackberries remain, I will put them in the dessert.

Yes. Both are grammatically correct.

• Si quedan moras, las pondré en el postre.
• Si quedan moras, pondré las moras en el postre.

But Spanish usually prefers the pronoun once the noun has already been mentioned, because it sounds more natural and less repetitive.

So las pondré is the more natural choice in most contexts.

Because poner has an irregular future stem:

• infinitive: poner
• future stem: pondr-
• pondré, pondrás, pondrá, pondremos, pondréis, pondrán

Many common verbs have irregular future stems like this:

• tener → tendré
• salir → saldré
• venir → vendré
• hacer → haré
• decir → diré

So pondré means I will put.

The future is used because the speaker is talking about a possible future action:

• Si quedan moras, las pondré en el postre.
• If there are blackberries left, I’ll put them in the dessert.

You sometimes can use the present in Spanish to talk about the future, but here the future tense is the most straightforward and natural choice.

Compare:

• Si quedan moras, las pondré en el postre. = clear future plan
• Si quedan moras, las pongo en el postre. = possible in conversation, but more informal or context-dependent

For learners, the safest pattern is:

• Si + present indicative + future

En el postre means in the dessert or into the dessert: the blackberries are being added as part of the dessert itself.

• las pondré en el postre = I’ll put them in the dessert

By contrast, de postre usually means for dessert or as dessert:

• Tomamos fruta de postre. = We have fruit for dessert.

So here:

• en el postre = inside / as part of the dish
• de postre = as the dessert course

Yes. That is a very natural interpretation.

In everyday English, this sentence often implies:

• If there are any blackberries left
• If there are some blackberries left over

That idea of left over / remaining comes from quedar.

If you wanted to make that idea even more explicit in Spanish, you could say:

• Si sobran moras, las pondré en el postre.

But si quedan moras is completely natural.

Yes. Spanish allows both orders:

• Si quedan moras, las pondré en el postre.
• Las pondré en el postre si quedan moras.

Both mean the same thing. The version with si quedan moras first puts the condition up front, which is very common.

Also note the comma:

• When the si-clause comes first, a comma is commonly written.
• When it comes second, no comma is usually needed.

In standard Peninsular Spanish, moras commonly means blackberries.

That said, berry vocabulary can vary a bit by region, and English berry words do not always match perfectly across Spanish-speaking countries. But for Spanish from Spain, moras is the normal word you would expect for blackberries.

Not usually in this sentence.

• en el postre = in the dessert
• al postre would usually not be the natural choice for meaning put them into the dessert itself

You use a with poner for destinations in some contexts:

• Ponerlo a la mesa is not natural; instead you would say ponerlo en la mesa.
• Similarly, ponerlas en el postre is the natural phrasing if they are going into or onto the dessert.

So en el postre is the best option here.