Eu preciso de muita água depois do treinamento.

Because the verb precisar is commonly used as precisar de + noun in Brazilian Portuguese when it means to need.

• Eu preciso de água. = I need water.
• Ela precisa de ajuda. = She needs help.

In everyday Brazilian Portuguese, this de is very common and expected.

You may sometimes see precisar used without de, especially in more formal writing or with another verb:

• Preciso estudar. = I need to study.

So in your sentence, preciso de muita água is the normal way to say I need a lot of water.

Yes, you can absolutely say:

• Preciso de muita água depois do treinamento.

Portuguese often drops subject pronouns because the verb ending already shows who the subject is.
Here, preciso clearly means I need.

Including Eu adds emphasis, clarity, or contrast:

• Eu preciso de muita água, mas ele não. = I need a lot of water, but he doesn’t.

So both are correct:

• Eu preciso... = slightly more explicit/emphatic
• Preciso... = very natural in conversation

Because água here is being used as an uncountable noun, like water in English.

When you talk about a large amount of something uncountable, Portuguese usually uses:

• muito / muita + singular noun

So:

• muita água = a lot of water
• muito leite = a lot of milk
• muita comida = a lot of food

You would only use the plural in special cases, such as different types or poetic/literary uses:

• águas minerais = mineral waters / types of water

In normal everyday speech, muita água is the standard form.

Because muito changes to match the noun in gender and number when it means many/a lot of.

Here, água is a feminine singular noun, so you use:

• muita água

Compare:

• muito tempo = a lot of time
• muita água = a lot of water
• muitos livros = many books
• muitas pessoas = many people

Even though água starts with a, it is still feminine.

Yes, água is feminine, and agreement is feminine.

Examples:

• a água
• muita água
• água fria
• esta água

A detail that often confuses learners: singular feminine nouns beginning with stressed a sound sometimes take o/a-like article patterns that can look unusual in Portuguese grammar discussions, but the noun is still feminine. In normal learning terms, the important point is:

• Treat água as feminine
• Use feminine agreement: muita, fria, esta, etc.

So in your sentence, muita água is correct because água is feminine.

Do is a contraction of:

• de + o = do

So:

• depois de o treinamento becomes depois do treinamento

This is very common in Portuguese. Other common contractions are:

• de + a = da
• de + os = dos
• de + as = das

Examples:

• depois da aula = after the class
• antes do jantar = before dinner

So depois do treinamento literally means after the training.

Portuguese uses articles much more often than English does.

So where English might say:

• after training

Portuguese often prefers:

• depois do treinamento
• depois do treino

The article makes the phrase sound more natural and definite in Portuguese. It often refers to a specific training session or the training in that context.

You may hear shorter alternatives depending on context, but depois do treinamento is very natural Brazilian Portuguese.

Both relate to training, but they are used a bit differently.

• treino is very common in everyday speech, especially for sports, workouts, and practice sessions
• treinamento can sound a bit more formal, structured, or general

Examples:

• Depois do treino, eu tomo água. = After training / after practice, I drink water.
• O treinamento da equipe começa às 8. = The team’s training starts at 8.

In many contexts, especially fitness or sports, Brazilians often say treino more naturally than treinamento.

Yes. Após o treinamento also means after the training.

The difference is mainly in style:

• depois do treinamento = more common in everyday speech
• após o treinamento = a bit more formal or written

Both are correct, but for casual spoken Brazilian Portuguese, depois do treinamento is usually the more natural choice.

Yes. Preciso can come from two different words:

1. precisar (verb) = to need

   • Eu preciso de água. = I need water.

2. preciso (adjective) = precise / exact

   • O número não é preciso. = The number is not precise.

In your sentence, preciso is clearly the verb form of precisar because it is followed by de muita água.

The given word order is very natural:

• Eu preciso de muita água depois do treinamento.

You can change it a little for emphasis, but not every change sounds equally natural.

Possible variations:

• Depois do treinamento, eu preciso de muita água.
• Eu preciso, depois do treinamento, de muita água. (more marked, less common in casual speech)

The most neutral and natural version is the original one.

A very natural everyday version would often be:

• Preciso de muita água depois do treino.

Why?

• dropping Eu is common
• treino is often more conversational than treinamento

Your original sentence is correct and natural, but this shorter version may sound even more like casual spoken Brazilian Portuguese.