This is not true, as modules can be either public or private, depending on your needs and preferences. You can use the Terraform Registry to publish and consume public modules, or use Terraform Cloud or Terraform Enterprise to host and manage private modules.

The correct syntax to pass a variable from the root module to a child module isservers = var.num_servers.
Terraform uses dot notation to reference variables.
References:
Terraform Variables

Terraform.tfstate
Explanation:
The name of the default file where Terraform stores the state is terraform.tfstate. This file contains a JSON representation of the current state of the infrastructure managed by Terraform. Terraform uses this file to track the metadata and attributes of the resources, and to plan and apply changes. By default, Terraform stores the state file locally in the same directory as the configuration files, but it can also be configured to store the state remotely in a backend. References = [Terraform State], [State File Format]

Terraform Cloud includes several features designed to enhance collaboration and infrastructure management.
Two of these features are:
* A web-based user interface (UI): This allows users to interact with Terraform Cloud through a browser, providing a centralized interface for managing Terraform configurations, state files, and workspaces.
* Remote state storage: This feature enables users to store their Terraform state files remotely in Terraform Cloud, ensuring that state is safely backed up and can be accessed by team members as needed.

You can install third party plugins using terraform init, as long as you specify the plugin directory in your configuration or as a command-line argument. You can also use the terraform providers mirror command to create a local mirror of providers from any source.