Does Home Assistant work without internet?

As long as your local network stays up and your integrations don't depend on an external service you should be able to continue to use it. When your WAN connection is down what kind of issue are you having when trying to connect locally? Apr 12, 2021

Do you have to pay for Home Assistant?

Home assistant is free to download and to use, to run home assistant you need to buy hardware that can start from $70 for a Raspberry PI 3B+ kit to $140 home assistant blue.