Quem quiser provar a melancia pode pegar um pedaço depois do almoço.

Because quiser is the future subjunctive of querer.

In Portuguese, after quem when you mean whoever / anyone who / the person who, Portuguese often uses the future subjunctive if the idea is open, indefinite, or conditional:

• Quem quiser = whoever wants to
• Quem puder = whoever can
• Quem souber = whoever knows

If you said quem quer, it would sound more like who wants...? in a direct-question-like way, not the same structure as whoever wants to.

So:

• Quem quiser provar a melancia... = Whoever wants to taste the watermelon...

The future subjunctive is very common in Portuguese, much more than in English.

It is often used when talking about something that may happen in the future, especially after words like:

• se = if
• quando = when
• quem = whoever
• onde = wherever

Here, quem quiser refers to any person who may want to taste the watermelon. The speaker is not talking about a specific known person, but about whoever ends up wanting to.

Other examples:

• Se você quiser, eu posso ajudar. = If you want, I can help.
• Quando ele chegar, a gente come. = When he arrives, we’ll eat.
• Quem puder vir, venha cedo. = Whoever can come, come early.

So quiser fits perfectly because the sentence is about a possible future desire.

Because quem is grammatically treated as singular in this kind of structure.

So you get:

• Quem quiser
• Quem puder
• Quem chegar primeiro

Even if the real-world meaning could refer to many people, the verb usually stays in the 3rd person singular.

That is why it is:

• Quem quiser provar... pode pegar...

not:

• Quem quiserem
• Quem podem

Yes. Provar has more than one meaning in Portuguese.

Common meanings include:

• to taste / try food
• to try on clothes
• to prove something

In this sentence, because the object is a melancia, it clearly means:

• to taste the watermelon

Examples:

• Quero provar o bolo. = I want to taste the cake.
• Ela provou o vestido. = She tried on the dress.
• Ele provou que estava certo. = He proved that he was right.

So learners need to rely on context.

Yes, in many situations you could.

• provar a melancia
• experimentar a melancia

Both can mean to taste / try the watermelon.

But there is a slight tendency:

• provar is very natural for tasting food
• experimentar can also mean to try, but it is a bit broader and can be used for experiences, products, ideas, etc.

So this sentence sounds especially natural with provar.

Portuguese uses definite articles much more often than English.

So where English might say:

• taste watermelon

Portuguese often says:

• provar a melancia

Here a melancia can mean:

• the watermelon
• watermelon, referring to the watermelon being served or available in that situation

This is very normal in Portuguese. It does not always have the same strong the feeling that it has in English.

Um pedaço means a piece or a slice/chunk, depending on context.

Since the sentence is talking about watermelon, um pedaço naturally means:

• a piece of watermelon

Portuguese often leaves out the repeated noun when it is obvious from context.

So:

• pode pegar um pedaço
  literally: can take a piece

The listener automatically understands a piece of the watermelon.

Here pode pegar means something like:

• can take
• may take
• is welcome to take

Pegar is a very common verb with many meanings, including:

• to take
• to grab
• to catch
• to pick up

In this context, it means to take oneself a piece.

So the sentence is not about physically grabbing in a rough way. It is just a natural way to say that someone is allowed to help themselves.

It can suggest both.

Literally, pode is often translated as can, but in many everyday situations it also expresses permission, which English often expresses with may or can.

Here:

• pode pegar um pedaço = can/may take a piece

In natural English, this might be translated as:

• can take a piece
• may take a piece
• is welcome to take a piece

So the idea is not mainly about ability. It is about permission or invitation.

Because Portuguese often omits subject pronouns when they are not necessary.

In this sentence, the subject is already expressed by quem quiser:

• Quem quiser provar a melancia = whoever wants to taste the watermelon

So Portuguese does not need an extra pronoun before pode pegar. The idea is already clear.

This is very common in Portuguese and usually sounds more natural than inserting an unnecessary pronoun.

Depois do almoço means after lunch.

The do is a contraction:

• de + o = do

So:

• depois de o almoço becomes depois do almoço

This is a standard contraction in Portuguese.

Other common ones:

• de + a = da
• em + o = no
• em + a = na

So:

• depois do almoço = after the lunch / after lunch

In English we usually just say after lunch, but Portuguese commonly uses the article here.

Usually almoço means lunch, the meal.

So depois do almoço most naturally means:

• after lunch
• after the lunch meal

In everyday use, it can also loosely imply after lunchtime / after we’ve eaten lunch, depending on context.

So the phrase is flexible, but the core meaning is the same.

Yes, Portuguese allows some flexibility.

For example, you could also say:

• Depois do almoço, quem quiser provar a melancia pode pegar um pedaço.

This puts depois do almoço first for emphasis on time.

The original order is completely natural, but moving the time phrase to the front is also common.

Here it is more like whoever wants to or anyone who wants to.

That is an important distinction.

• Quem quer provar a melancia? = Who wants to taste the watermelon?
  This is a direct question.

• Quem quiser provar a melancia pode pegar um pedaço. = Whoever wants to taste the watermelon can take a piece.
  This is a general statement.

So quem quiser is indefinite and open-ended, not a question.