Graphs seem to jump becouse the app tries to use all available screen space and zooms in maximizing your graph height. If you look closely, values might have several decimal places and the whole screen height might only show 0,05 degrees for temp, so you really see just the background noise.
That happens in graph auto mode, you can set it to manual and pinch to zoom it where ever you want to.
I don’t have my mooshimeter with me right now, so I’m not sure where it is easiest to find fw version, but it should be easy to find it, as there is several places for it. If I remember correctly, it is on the search screen when you start the app.