Learn Portuguese (Portugal): Boa viagem! — Obrigado, igualmente. - Have a good trip!

In Portuguese, almost all nouns ending in -agem are feminine, such as a viagem (the trip) or a mensagem (the message). Because of this, the adjective must agree and become boa.

Where is the word for "have"? Why isn't it translated as "Tenha uma boa viagem"?

You can say Tenha uma boa viagem, but Portuguese speakers usually drop the verb in standard well-wishes. Saying just Boa viagem! is the most natural way to express this, just like saying "Good morning!" in English.

If I am a woman saying this to a man, do I say obrigado or obrigada?

You would say obrigada. The word for "thank you" always changes to match the gender of the person speaking, regardless of who is listening.

Does igualmente literally mean "you too"?

It literally translates to "equally". However, in everyday conversations, it is the most common way to say "you too", "likewise", or "the same to you" in response to a greeting or a well-wish.