Complex keyword phrases

Hello!

I have a site for ESL (English as a Second Language) learners. My main target are Brazilians who speak Portuguese and are trying to learn English. I would like to add articles to our site that would tap into keywords they are searching for, but I am not sure how to go about discovering what they are searching for in terms of phrases. Let me explain with an example:

Let's take the phrasal verb "cheer up", for example, which means to "feel encouraged and happier". In Portuguese , it could be translated as "animar-se" or "animar alguém".

How can I find out if they are searching for sentence like:

- O que quer dizer o phrasal verb "cheer up"? [translation: what does the phrasal verb "cheer up" mean?]
Or
- Como se diz "cheer up" em português? [How to say "cheer up" in Portuguese]
Or
- O que significa "cheer up"? [another way of saying "what does 'cheer up' mean]
Or
- Como traduzir "cheer up" em português [How to translate "cheer up" into Portuguese?]
Or
- Como dizer "animar-se" em inglês [How to say "animar-se" in English]

How can I find out what way Brazilians are searching for these kinds of expressions?

And then, after that, how can I find out which particular expressions/phrasaes/grammar they are searching for?

Do you see what I mean? Not only do I need to find out *what* phrases and grammar they are searching for, but *how* they are searching for them.

Do you guys have any suggestions on how to find out this kind of information?

Your help will be much appreciated! Thank you very much!