Yes, the grades depend on the selected browser. The gzip and image compression checks both require access to the response bodies and can’t be calculated otherwise. I may be able to work out some UI that reports the other grades that only depend on the request metadata (timings and headers) if it would be helpful.
I forgot Firefox doesn’t support bodies so it is also not supported there yet. It used to work because the older agents didn’t require browser support and intercepted the raw network data but it was Windows-only and fragile (and will no longer work with Chrome). The Firefox dev team is working on exposing better remote debugging support which should make it possible when it becomes available.
The missing ssl checks is a different problem. The Firefox agent uses the supported request details from an extension but also parses the internal logs which have much richer details. It looks like the logs processing broke (likely a change in the messages with a Firefox update). Looking into it now.