Don't worry about absolute pitch too much, a majority of it is based on critical period. Based on scientific research, it'll be nearly impossible to develop absolute pitch to the degree that those who developed it at an early age. I think that most musically inclined often are able to think of one note's pitch in their head and then find other notes using relative pitch, anyhow. With that remark, relative pitch is generally more important than absolute pitch anyway.
In most cases, you just need to find the starting note and use relative pitch the find other notes in a piece of music. You could even write as you hear it and if your absolute pitch was off, you could simply transpose afterwards. I think that the best way to be able to improve relative pitch is to associate intervals or whatever with songs you know. To improve listening to scales, listen for Whole Steps and Half Steps. Listen to a few Whole Tone and Chromatic Scales to fully grasp the Steps and then move on to other scales. Major is W W h W W W h and Natural Minor is W h W W h W W. To differentiate the Minors, the Harmonic Minor sounds like a Natural Minor, with the exception of the Step between the 7th and 8th Notes being Half (if you listen to Whole Tone and Chromatic a bit, noticing this should be easier). As for Melodic Minor, the beginning sounds like any typical Minor Scale, but its last 3 notes sound like a Major Scale when ascending. If the scale is being played ascending and descending though, Melodic Scale is much simpler, since you simply need to hear for a change of the 6th and 7th notes on the way down.
