This is where just being in Japan is going to help you a lot, although if you want to improve your listening quickly/past a certain level you will need to make some effort.

Back when I was in university in my home country I failed the listening section of JLPT 3, because I had never been to Japan or really heard native speakers talk. It took me years to get around to taking level 2, but by that time I had been in Japan 6 years and listening was by far the easiest part of the test. Just hearing people speaking around you, watching TV and listening to the various announcements you hear will start to train your ear in no time.

I have to agree with this. Listening will definitely be the easiest part once you have been in Japan for a while. The level of grammar and vocabulary used in the listening part is far below what will be in the written section. If you`re used to listening to Japanese (as you will be after a bit of time in Japan) it will feel ridiculously easy.

The best way to practice listening is to, well, listen to real life... And participate if at all possible. Outside of Japan, normal everyday boring small talk (in Japanese) is not something you encounter much... But in Japan? Everywhere.

Regarding the medical check, I just had to get a full physical. That was a physical, urine and blood check.

Talk to your doctor about getting 6 months of prescription to take with you.