National Health Payments

Which month marks the final monthly payment of national health contributions for 2017-18? Is it April 2018 or May or later? And the next year (2018-19) begins from which month?

yearly calculation: it starts from April and ends in March (next year).
your yearly (total) fee will be decided in May. (your last year's income is fixed after March 15. the tax office informs your income to the city office. they calculate residential tax and health insurance and inform you the amounts in May.)
thus, there are two ways to pay it, depending on cities.
1. in April and May, they take temporary amounts. after your last year's income is fixed, they re-calculate the fee. they will charge the re-calculated amount from June to March (next year).
2. in April and May, they don't take money. the total (yearly) amounts is divided into 10 portions. you pay from June to March (next year). be noted that it does not mean no fee in April and May.
if you move to another city,
they will re-calculate to adjust the difference between your "actual" payments and your "real" monthly fees. they will send you the final bill to your new address (or withdraw it from your bank account). of course, if they took too much, they will give you a refund.

Ken

That's excellent info, thank you.

Could I further ask your advice about this below?

For family reasons, I might have to go back home next year and may not be in Japan from all of March to end May, expecting to return by 1st June. My NHI is usually auto deducted from my bank, but could I cancel/stop this during this 3 months period (my payments are over 12 months)? It amounts to around nearly 250k, so not keen to pay whilst I'm clearly not around to benefit from using the service.

Then, when I return I would either start auto deductions again, or even pay some other way, such as conbini if that is possible.