Regarding the LN backend, yes, an LN configuration is required. Currently, PurrMint supports LNbits, which can be hosted
As for whether the mint can be accessed online, the answer is yes, it can be
1. First, enabling Android foreground service ensures that the mint stays online most of the time
2. Second, you can use Tor to enable access to your mint via the Onion service
3. Alternatively, you can use NIP-74. For more details, refer to my write-up here: https://github.com/heathermm55/nips/blob/master/74.md
