1. The genders don't matter nearly as much as non-speakers think they do. If you talk to your bank, it doesn't matter if you ask about "der Konto", "die Konto" or "das Konto" (the last is actually correct), you will be able to communicate quite fine. Unlike French, there are very few words where changing the gender has a different meaning - das Bund/der Bund (the bundle/the association) is the only one I can think of off-hand. Same with adjective declinations - "das verbundenes Konto", "zum verbundene Konto", "ein verbundenen Konto" are all wrong and will grate on the German ear, but will all be understood.
2. I agree absolutely with not trying to map German propositions to English ones. One of the things that improved my German a lot is learning the verb + proposition combinations - "ich denke an...", "ich freue mich auf...", "ich helfe dir bei ..."
3. There is an amazing amount of structure in German words which you start to see after you have basic vocabulary, which makes it easier to guess at the meaning of words you've never come across before. For example: das Mitleid - "mit" means with, and "leid" would be related to the verb "leiden", to suffer. So you'd have "with-suffering", which makes it possible to guess the actual meaning - "compassion" or "pity". This of course gets extended far further with German's compound words.