I'm not sure about using an external microphone as every Android App I've tested on my phone will not use the external microphone so I can't know for sure if it's just my cheap Chinese Android phone, or if it's a software Android App limitation. However my favorite Android Apps for "music production" or "idea capture" and "song creation", etc... are in no particular order:
Caustic 3: Not for "Audio Recording", but if you are trying to write down song ideas/structures using a Piano Roll/MIDI then I haven't found any better software to achieve this on the go. I use it to write songs while on vacation without access to a computer. It's more along the lines of a Tracker software like the old PC software versions of Reason, FrootyLoops, ReBirth, etc...
Audio Recorder: Sony Mobile's simple Audio Recorder is what I use for recording all of my "quick ideas". It's free and saves all of my recordings to my SD card which saves me the hassle of having to manage my "internal storage" all the time.
n-Track Studio Music DAW: I have not used this that much but it is the only 4-track/Multitrack recorder that I've found that allows for "live monitoring" with my phone. I use this when I need to record vocals quickly (on an external recorder, mind you, as I can't get an external microphone to work with my phone/android software), but need to monitor the backing track as well as my vocals, and this works great for that, I can even add some reverb to the vocals (which helps me when recording for some strange reason) while I monitor live. The recorded vocals in the App are later used to match/sync my externally recorded vocals later. I've linked to the free version of n-Track here, but they do offer a feature packed version for $30, but the demo works perfectly for my needs and might for you too. I don't know all the limitations of the demo version, but it may be fine for what you're trying to accomplish. Otherwise...
J4T Multitrack Recorder: Is a dead simple, and inexpensive 4-track recorder. I use it to record some simple guitar parts (while plugged into my little Laney Mini-ST and using the Tonebridge Guitar Effects Android App as my monitoring device, because unfortunately this little 4-track App has no live monitoring) however I'm not sure if it's recording the DI signal from my Laney amp connection or if it's just the phone's microphone recording (guess I should try singing along with my guitar next time to test it out...) but sadly it won't record your killer tone that you're using in the Tonebridge App.
Hope someone finds this information useful even if it isn't exactly what you're looking for.
I use Easy Voice Recorder Pro (by Digipom) with a TOQIBO lavalier microphone on an Honor 8X. The microphone has a TRRS plug and is seen as a headset so with a direct connection there's no audio playback while it's plugged-in.
Try Easy Voice Recorder first to make sure it works with your hardware then consider if you want to upgrade to the Pro version for e.g. 48kHz 16-bit WAV recording capability. I use my setup for recording simple voice commentary and it works very well for my needs.