Japanese Grammar Guide（日本語の文法）
A helpful tip for those having trouble with grammar:
- Listen to the sentence
- Shadow the sentence by saying it aloud, as close as possible to the pronunciation
- Say the sentence again, but slower, and keep track of the position of the nouns and verbs
- Repeat the sentence once more at a regular pace, while translating it mentally
- Type your answer and note your mistakes
- Rinse and repeat
Just remember that you don't have to stress so much on grammar, since it is learnt through speaking and practice. Don't think of the sentences as individual pieces, but think of them as a single meaning. Do this for all lessons and you will feel the grammar soak into your brain.
I really recommend focusing at vocabulary before starting with grammar. If you know what words mean, you can try at least to guess what a sentence means. After that, If books are not an option for you, I recommend Imabi and Kim Tae's Guide to Japanese for grammar. You will need to learn along the way general grammar things that can be confusing in any language, such as subject, topic, agent and so on. Take your time. Don't try to remember it, just understand the general rules. The site you put a link for also looks very nice, examples are great for truly understanding the context of using a particle and where the hell you are supposed to place it. Also, try reading some comics at Xoy, and if you can try to find raw manga with Furigana. Watch some Youtube videos, even if you don't understand anything. I personally love Kinoshita Yuka as I love seeing food and there are Japanese subtitles available on her videos. The language she uses is also not too hard. At viki.com you can watch some Japanese (and some other East Asian) shows with Japanese subtitles, but they are not too common and it's more intermediate level.
This is a bad idea. It's like learning English through Disney movies. You will be able to sing about your inner worries and joys, but you won't be able to ask a stranger where you could find a toilet.
EDIT: Clarification: Anime and music are good for immersion, but not as a learning resource alone.