I'd be happy to provide with you some insights about estimates and invoices in QuickBooks Desktop.
Estimates generally are used at the start of a transaction. Typically an estimate will be presented before a sale has finished, or before any money is due. Invoices, on the other hand, are issued at the end of a transaction when money is owed by your customer.
After converting an estimate into an invoice, you'll still be able to see the estimate in customer's profile with the same information.
These are not Converted; they both still exist and are Linked or Not.
Let's review: I can use an estimate for my own internal tracking and comparison reporting as a Baseline Scope of work for Price, or as a Quote to the customer. I can invoice from Actual or Billable time & costs, or from the Estimate which is called Progress Invoicing, or all of it at once.
"What happens to invoices that turn into invoices? Are they still out there as an estimate"
Yes, see them on the transactions listing as Activity for that name.
"or do they move to a different type of status?"
If you use the function to Invoice "from" Estimate, that will show the Estimate in progress or even Inactive = done. Or, you can Make Inactive, manually, such as, I invoiced from Sales Orders or Billable time and costs, and now the job is done, I've done all my comparison reporting, and I "make inactive" the Estimate = done.
"If I change the estimate on the invoice, does that impact the original estimate?"
No; you manually changed the Sale, not backwards updating the estimate. And you don't want to affect the Estimate, because that sort of defeats the usefulness of the reporting Estimates vs Actuals.