MSFS Licenses

Yes to both questions.

Yes you can use your current DVD purchase to download the sim, you don’t need to use the discs.
The MSFS support article links to this procedure from Aerosoft:

https://helpdesk.aerosoft.com/hc/en-gb/articles/4573598584477--This-code-has-already-been-redeemed-when-reinstalling-or-installing-to-a-new-PC

Your purchases are also tied to your account.
When the sim is up and running, you simply go to the Content Manager and reinstall your purchases.