Leaving Japan

I have stayed here in Japan for a year as a student visa. I'm scheduled to leave in 10 days (from today)since my visa is about to expire. My problem is, is it still ok to apply for the moving out notification in the city/ward office even if it's only more than a week before my flight? Actually I was planning to do it last week but i was too occupied with the JLPT exam that i totally forgot it. Please help!!!

And one more thing i want to ask, do i have to pay the months that i wasn't able to pay in the health insurance? School was too busy and I'm also struggling with my budget this whole year so i have only paid a few months worth. I am waiting for your responses, thank you!

Note: i have already notified the apartment landlord two months ago so there's no more problem about the apartment. I'm only worried about the city/ward.

Go to your city office and ask them the exact same questions you have asked here.

Reply to above comment: I wouldn't waste my time asking here if I could have just gone to the city hall and ask them. Sorry but I only speak a little bit of Japanese that's why I'm asking for a little bit of help here. Your nonsense doesn't help. I just wish to get a little bit of idea so I would know what to expect.

It's nice that you worry about your financial obligations to city hall, but I honestly don't imagine you would be top of their list to pursue across international borders for a month or so missing payments.

If you do as Max said, just think of the consequences/probabilities . Your name maybe put on the watch list for non-payment.
Think what it may or may not affect your future visa application.
Also it will just add to the stereotyping of gaijin running off, with no responsibility paying off what it is due.

As for Firas response, well sometimes but Firas do have a point there. Go to your municipal office, maybe ask for foreigner support, some do provides.

Leave nothing behind except memories unless you want those to haunt you back in the future,

Go to the city hall and do the moving-out notification thing, you can even do it the day before leaving, don't worry about that. But make sure you do it, you can run into trouble if you don't do it and come back to Japan (it happened to me and I had to do double the paperwork when I came back).
Oh and do pay your health insurance...