I use one of the Android phone apps for ear training, and one of the drills is to recognise chord inversions, this includes minor/major chords and also dominant 7-th chords. They conventionally label inversions with numbers from 0 to 3 with 0 being the root position.
I trained myself to recognise the harmonic versions of the chords by listening to the top note, so that the recognition of the inversion becomes equivalent to recognition of a kind of melody.
One of the advanced exercises is recognising inversions of the open chords, and they contain sometimes 5-6 notes. My strategy with the highest note failed because it seems that this is not a proper definition of the chord inversion.
Question 1. Conventionally speaking, what does it mean - an inversion number of the chord in open position? Does such a convention exist?
I suspect that there is either no convention, or the program assumes the position of the root note, but I don't know any reference.
Question 2. Is there any practical advice to recognition of the inversions of the chords, especially in open positions?
Currently my way is just a "dumb practice", i.e. trying to listen and recognise. But I suspect that there may exist more useful exercises designed especially to learn how the chord is presented.