As a civil servant, you remain fully covered by the social security system of your employer in your home country. You should claim child benefits in your home country.
As a civil servant, if you become unemployed, you can choose to register as a jobseeker either in the country which employed you or in the country where you worked.
If you choose to remain in the country where you worked, you must register as a jobseeker there. You will be treated like a national. You need to apply for a U1 form (or an E 301 form) from the national employment authority of the country which employed you.
If you choose to return to the country which employed you, you must register directly as a jobseeker there.
As a civil servant, when you are seconded abroad by your employer, you need to apply for an S1 form (or an E 106 form) from your health insurance in order for you and your family to have access to healthcare during your stay. Once you have found a place to stay, submit your S1 form (or E 106 form) to the health insurance authority of your choice (if there is a choice) in your new country.
Find out about the healthcare system of the country where you now work: it could differ greatly from the structures you are familiar with in your home country.
In order to receive medical treatment locally (in the country where you are posted), you should ask your insurance authority (in the country where you usually work) for a DA1 document giving details of the accident or sickness. You should then present the DA1 document to the insurance authority in the country where you are posted.
Income replacement for any time off is paid by your insurance authority (in the country where you usually work).