Hanna, I was really glad to hear you say all this.
I have the same problem with nouns and the declensions of cases.. I've been studying Russian three years, and everytime I think I've got cases understood, I stumble across an exception and feel I have to start out back at Square 1 to understand things right.
It reminds me of when I was 12 years old, trying to learn QBASIC through trial and error *(there was no "internet" to ask, hehe)* .....
Please don't let frustration bother you in this. And don't give up. We may learn best (and more comfortably) through rote memorization, through committing these patterns to memory. But when that fails (as it often has me), a different kind of learning can pick up in its place. ... Have you seen a movie called Memento? Its theme is amnesia and it mentions a lot about this second sort of learning - I think about it a lot when I consider my rocky road in learning Russian. =)