Travel insurance and time needed to get the visa from the application day

Hello
We are a family of four (Cypriot Citizens) travelling to Beijing from Cyprus for 7 days vacation. Do we need an international travel insurance in order to get a visa? We booked our tickets online and booked our hotel online. What exactly is this insurance? Where to get it from?
Another question is how many days approximately are needed in order to receive the visas (from the day we apply to the embassy ?)

Thanks
Louiza