Eu gostaria de uma salada sem pimenta, mas com bastante molho.

Eu gostaria is a more polite, softer way to make a request. It is similar to saying I would like in English.

• Eu gostaria de uma salada... = polite / customer-service style
• Eu quero uma salada... = more direct, like I want a salad

In Brazil, eu quero is not always rude, but eu gostaria sounds more courteous, especially in restaurants.

Because gostaria is often followed by de when you say what you would like.

So:

• Eu gostaria de uma salada.
• Eu gostaria de água.

This is a very common structure in Portuguese. English speakers often want to say something like Eu gostaria uma salada, but that sounds incomplete in Portuguese. The de is needed here.

Yes. In Brazilian Portuguese, subject pronouns are often omitted when the verb already makes the meaning clear.

So both are natural:

• Eu gostaria de uma salada...
• Gostaria de uma salada...

Including eu can add a little emphasis or clarity, but it is not required.