Could also simply say "compact" instead of "small mirror", if it refers to the makeup nitrous commonly kept in purses
That's too tenuous a translation here. With more context it works, of course. If someone asked "Do you have mirror?" and you answered "I have a compact", you are indeed telling that person that you have a small mirror, but to anyone else who didn't hear the question you are simply saying you have a compact.
What do you mean by "nitrous", is that some auto-spelling-correction artefact?
Yes, it should have been most. The phone app does't seem to let us edit posts?
I translated the sentence as "I have a little looking glass" and it was not accepted. Am I too old-fashioned?
This dictionary thinks so: http://www.oxforddictionaries.com/definition/learner/looking-glass
I'd ask for "looking glass" and "looking-glass" to be accepted if I were you - no harm done.
Why pequeno did not come before espelho? Do nouns go before adjectives in Portuguese?