Nothing is 100% secure, I guess you need to minimise the risks. If you have to use an untrusted computer, better use your mobile than entering the keys on that computer.
If the WIFI network is being sniffed, it's still OK because the keys are not being transmitted between the wallet and the frontend only the request and the signed content.
As for loosing the phone and the person brute forcing into the device, even if they read the disk, the keys would be encrypted in the local storage of the wallet app, I don't think Hive Keychain stores keys in plain text (@stoodkev let me know if I'm wrong). Some phones also have a protection system where you can remotely wipe the phone or it will self-wipe under brute force.
@arcange can also give more details regarding the security side of HiveAuth.
The keys stored are encrypted at least once with the PIN, twice if using biometrics.