Just memorizing all the on/kun yomi for each kanji does not really work, it's better and more efficient to increase your vocabulary and see what kanji is used and how it is pronounced at the same time.
I do not know which side of Asakusa you're residing, there are Japanese language classes by volunteers both in Sumida-ku and Taito-ku, here's the list.
Volunteer Japanese-Language Classes of Tokyo
Go to the ward office and you should be able to get more detailed information.
Those classes are basically free (might need some fee for text books etc.) and good but since most of the cases they are taught by volunteer teachers who are not necessarily qualified and there're limits what you can learn free of charge.
Just my 2 cents.
Are you here for a short visit or is Japan going to be your permanent home now?
my permanent home now. Got Japanese Passport recently.
Then, yes, you need to listen to that CD and anything else you can get your hands on over and over again. You have a lot of catching up to do. You have a lot of very hard work to do, especially with the kanji. You have my full sympathy, but unfortunately there is no shortcut for learning or any substitute for spending hours and hours diligently working. I want to encourage you to do your best. You don't want to spend your life here illiterate.
Any prescribed hours of learning and having fun?
I also agree that trying to memorise kanji readings separately from learning vocabulary is a waste of time. I tried it, and it was the most mind-numbing and dispiriting of experiences.
I bought manga too today lol I think that would help me somehow.
if your goal is just to pass the exam for the mean time...
i can give you this advice..
i passed N5 last year.. and i can tell that its pretty easy on the kanji part...
1.kanji
2.grammar
3.reading
4.listening
that's the order of difficulty for me... 1 the easiest to 4 hardest...
but i took it here in the philippines.. i don't know if there's difference on which country you will be taking it...
anyways just memorize the kanji...
the exam will just be like 1. あめ(rain) then you'll choose which kanji it corresponds to
and the word there aren't that complicated its like maximum of 2 kanji only like 電車(densha)...
just memorize those 150 kanji and its basic meaning then you can easily perfect the kanji part...
That's quite a good order. But reading is not that bad if you understand what to do. Usually they ask you to interprete the text. IMO the hardest part is vocabulary, which require having a good knowledge of words. The easiest part is arranging sentence, which require only memorizing grammar structure.