How can you pull down a User's manager in a request offering?
You can use 'Additional fields' to gather the desired information as well.
A quick example is below:
You can use "Current User: Display Name" to set a read-only field to denote the user and pull the fields through that selection.
Define the additional fields you want to pull down.
Add a new field to the request offering, this will hold your additional data.
For the default value, select expression.
Find the additional field you want and drag it into the form.
Set the field to be 'Read only' if you don't want your users changing that value. You can also set the field to be 'hidden' so the users don't see it either.
The manager's name and email were correctly populated.