Perhaps we are obsessed with learning words because it's the easier problem to solve.
I think that depends on the person and/or language.
My Polish grammar knowledge is now pretty impressive, but I'm having a terrible time trying to remember words, so spend the majority of my time attempting to force memorisation with flash cards.
In a way it's kinda fun - I can go through pages of grammar exercises, conjugating and declining correctly, but with no idea of what Marta did in the past with 101 of somebody's somethings.
I'm delving into learning Polish myself but have been taking mostly a whole language, immersion approach. For example, when I was in Krakow I bought myself a book on CD and the book itself, so I can 'read' along as I listen. I use translation tools to put selected passages into English. I also spend time listening to Polish radio. I know at some point I will have to develop some discipline about tackling grammar in a systematic fashion the way you are doing, but for the moment I guess I'm content to as much as possible to get a feel for the language. Japanese is my second language and its challenges are almost completely different... anyway, good luck!
Quite often you can figure out the essence of the sentences even if you don't know all the words. Of course, you do need to have a basic vocabulary. While speaking/writing it is possible for you to convey what you want to without using complicated words. If you can simplify your thought and strip out all that's non-essential, you will be able to convey the essence of your thought.
However, if you don't have a grasp of the basic grammar you're prone to confuse the person you're talking to. If you're reading, then you lose the context.
Exceptions abound, but I have found this to be true quite often while studying French.
I think that depends on the person and/or language.
My Polish grammar knowledge is now pretty impressive, but I'm having a terrible time trying to remember words, so spend the majority of my time attempting to force memorisation with flash cards.
In a way it's kinda fun - I can go through pages of grammar exercises, conjugating and declining correctly, but with no idea of what Marta did in the past with 101 of somebody's somethings.