In my opinion, comprehending English and communicating in English ARE more important than memorizing grammar rules or having perfect English grammar. You will learn habits if you use English often. You don't need to always be consciously aware of every grammatical detail when you use English.
However, you should try to develop good habits and you should also try to understand the concepts of English grammar.
That's a good question. Vocabulary is flesh of a language while grammar is its skeleton =)
I'd say, learning words and phrases are primary. As soon as basic vocabulary is there, you can hone in on grammar.
As a learner of a few languages, I think it's really important to listen to and look for idiomatic phrases, set phrases which native speakers use and try to learn and copy them. This way you build a "template", a model in your head. And later, you can use them without thinking. Moreover, this way you make sure you don't make mistakes (unlike when you're trying to make up something of your own). This is similar to how we all learn our mother tongue: we learn vocabulary and listen to our parents and other speakers, don't we? :)
Henry, I think, it depends on your goals.
It is also can be changed with time because your goals can be changed.
Currently, grammar is important for me, but it wasn't like this before.