Explanation
TF_LOG_PATH specifies where the log should persist its output to. Note that even when TF_LOG_PATH is set, TF_LOG must be set in order for any logging to be enabled.
For example, to always write the log to the directory you're currently running terraform from:
export TF_LOG_PATH=./terraform.log
export TF_LOG=TRACE

In a parent module, outputs of child modules are available in expressions as module.<MODULE NAME>.<OUTPUT NAME>.
For example, if a child module named web_server declared an output named instance_ip_address, you could access that value as module.web_server.instance_ip_address.

Explanation
Outputs can be marked as containing sensitive material by setting the sensitive attribute to true, like this:
output "sensitive" {
sensitive = true
value = VALUE
}
When outputs are displayed on-screen following a terraform apply or terraform refresh, sensitive outputs are redacted, with <sensitive> displayed in place of their value.
Limitations of Sensitive Outputs
The values of sensitive outputs are still stored in the Terraform state, and available using the terraform output command, so cannot be relied on as a sole means of protecting values.
Sensitivity is not tracked internally, so if the output is interpolated in another module into a resource, the value will be displayed.

Explanation
The local backend stores state on the local filesystem, locks that state using system APIs, and performs operations locally.
Reference: https://www.terraform.io/docs/language/settings/backends/local.html

Explanation
If a resource successfully creates but fails during provisioning, Terraform will error and mark the resource as "tainted". A resource that is tainted has been physically created, but can't be considered safe to use since provisioning failed. Terraform also does not automatically roll back and destroy the resource during the apply when the failure happens, because that would go against the execution plan: the execution plan would've said a resource will be created, but does not say it will ever be deleted.