1. Do I need to use HOC or it's a new way to do this?

No, you don't need to use HOC as best technique.

Why? Starting from React v7.0, you can use functional-based components. From this version efficient is to use the the latest technique named HOOKS, which were designed to replace class and provide another great alternative to compose behavior into your components.

2. Do I need the Context.Provider or it's new Hook?

Hook like useContext() has a relation with Context.Provider.
Context is designed to share data that can be considered “global”.

The Provider component accepts a value prop to be passed. Every Context come with a Provider.

Context.Provider component available on the context instance is used to provide the context to its child components, no matter how deep they are.

3. Do I need to declare default value as a null or I can pass my Object right from context.js?

No, you don't need necessarily to declare a default value.

Example of defining the context in one corner of the codebase without defaultValue.

const CountStateContext = React.createContext() // <-- define the context without defaultValue

4. How can I use a new Hook instead of HOC in mine code?

index.jsx

import App from './App'

import Firebase, { FirebaseContext } from './components/Firebase'

const FirebaseContext = React.createContext(null)

ReactDOM.render(
  <FirebaseContext.Provider value={new Firebase()}>
    <App />
  </FirebaseContext.Provider>,
  document.getElementById('root'),
)

Root Component: App.js, where will be used data comes form context:

const App = () => {
    const firebase = useContext(FirebaseContext) 
    return(...)
}
export default App;