Well, there are normally two options with the situation. The first would be practicing to get down the rhythm and speed. That’s always tricky. The other would be doing an English cover and writing translyrics. That way, you can dictate how fast the lyrics go, and it should be easier because you know the language. Worst case scenario, you could use Audacity (or any other audio editing program) and slow down the instrumental.
Japanese romaji is usually very difficult to understand at first. It takes a lot of time and practice to be able to at least get most of the pronunciation correct. It also takes a lot of experience, or should I say practice again, to be able to read it at a pace where you can actually sing it with no problem. When I started singing Japanese songs, I was in the same exact situation as you. I could not keep up to the song, and did not understand how to read Japanese romaji correctly. Of course, I kept practicing and invested most of my time trying to learn how to read each letter in romaji. During this time, I also immersed myself in learning the Japanese language. Now I'm able to sing a lot of Japanese words without a problem. **Just know that Japanese romaji sounds as it looks.** For example, ohayo looks and sounds just like Ohio (one of the U.S. states). Another example would be gomen. You would say go-men, literally. And bigger words such as, arigatougozaimasu, can be quite tricky to get a complete grasp on. You can put spaces between certain parts of the word to get a better understanding on how to say it. Like this: arigatou go zai masu.
To be able to sing Japanese quickly is also very difficult. The language is a fast-paced one. Japan is also one of the countries that speak very quickly. In order for you to not get tongue-twisted when singing a quick song, make sure to start the song off in a slow speed (as slow as you want) and then gradually make your way back to the original speed. Like I said before, to be able to get a good grasp on how to say certain words/lyrics using Japanese romaji, you must practice or at least understand, how each lyric corresponds to the beat and sound of a music. Almost all the time, lyrics follow the music and by following the music, you're able to sing according to the beat of a certain song. I have more to say but it will be too long. Japanese is hard to learn, but don't give up. Practice makes perfect.
I’ve been in choir for 6 years, so i can speak from experience. We’re trained in breath support. An excersize to help you with that is breathing in a certain number of counts/seconds (EX: 6), then letting out your breath in the same amount of counts/seconds using he sound tss, tss, tss.