If you are receiving unemployment benefits from the country where you became unemployed, your health insurance will still work in other EU countries. You and your family will be entitled to treatment — but you will need to show your European health insurance card. If you do not have one yet, you can apply for one from your health insurance authority.
Find out about how the healthcare system works when you move to a new country. It could be very different to the one you are familiar with.
YES — transferring unemployment benefits to another country in order to look for a job there does not affect your social security entitlements or those of your family (health insurance, family allowance, invalidity or old age pension rights, etc.) in the country where you became unemployed.