Box 1: No -
Front Door can dynamically compress content on the edge, resulting in a smaller and faster response to your clients. All files are eligible for compression.
However, a file must be of a MIME type that is eligible for compression list.
Box 2: No -
Sometimes you may wish to purge cached content from all edge nodes and force them all to retrieve new updated assets. This might be due to updates to your web application, or to quickly update assets that contain incorrect information.
Box 3: Yes -
These profiles support the following compression encodings: Gzip (GNU zip), Brotli
Reference:
https://docs.microsoft.com/en-us/azure/frontdoor/front-door-caching