Anyone knows what this third party input method? And is it safe to use it since it's from an unidentified developer? It basically gives you a PinYin-like words prediction but for English
When macOS informs you that software etc is from an unidentified developer this doesn't necessarily mean it's unsafe. An unidentified developer simply means that the software has not been registered with Apple. There are many reasons why this may be the case (e.g. the software may date back to before Apple started registering developer IDs).

Regardless of the quality of the software, if it's not registered than recent versions of macOS will present you with a warning dialog when you try to launch it. Typically this message will identify the app and tell you it's from an unidentified developer, and it may ask you if you're sure you want to open it.

Unfortunately there is no way for anyone here to advise you if the software you're referring to is safe unless we know what the software is or who the developer is.