The progress with chord progressions is being very slow. Is it normal?
Is it ok to just stay with the cellphone app?
How much ear-training do I have to learn to be a decent pianist?
However, your aim should be to sing the melodies without any aid of another instrument. What you want to be able to do is to take a melody you have not previously seen or heard before and sing it, without hearing it played on an instrument. Instead of imitating pitches you hear from an instrument, you will be developing the ability to internally generate pitches. What does singing have to do with ear training? If you can internally generate pitches, it is much easier to recognize them when other instruments are producing them.
My question is about how long does it usually take to learn to hear chord progressions. Is it a reasonable goal to be able to identify 4 chord progressions with chords I to viio in about 8 months?
Now, no short cuts, or snake oil. Yes, transcribing daily is going to produce the best results, and "sing, sing, sing". You can add on transposing, improvisation, and sight reading as being helpful too.