The following piece is in key of Eb/Cm and I'm struggling to read it.
Firstly, the key is Eb so, the A is already Ab, does the accidental turn it into an Abb(G)?
Secondly, the Abb appears yet again in flat form, does it mean it will be an Abbb?(Gb)?
Source, Kent Hewit, My Funny Valentine
As others have written, those accidentals don't sum up. To understand, why they are in this bar, I think it helps to look at the bars before the one in question. So, here we go:
Firstly, the key is Eb so, the A is already Ab, does the accidental turn it into an Abb(G)?
Right before this, in the previous bar, is an A natural. Hence, the flat you ask about is a reminder to play Ab again.
Secondly, the Abb appears yet again in flat form, does it mean it will be an Abbb?(Gb)?
This is also a reminder not to play A natural, but Ab. This time, it is meant for the second voice (which consists of the quarter notes/crotchets).
As Tim correctly commented, both reminders are not really necessary, since a bar line in general cancels all accidentals of the preceding bar. In this case, the bar line cancelled the A natural.
No, and no. This could be considered a courtesy accidental. It belongs to the melody voice, which had an A-natural in the immediately preceding measure. Sometimes courtesy accidentals are notated in parentheses to indicate the note is already modified.
Actually the key is e flat; the accidentals do not add up to the key signature as already discussed in this question; if adding up was intended, a double flat would be required. Repetition of an accidental is also not changing something.
Courtesy accidentals (convention is to put them in parentheses) are quite untypical to appear for accidentals from the key signature (but since the a flat was natutalized in the bar before, it is a valid courtesy accidental); additionally the c flat is necessary.
Your question is rather muddled. "The following piece is in key of Bb and I'm struggling to read it. Firstly, the key is Eb...".
Don't tell us about the key signature, SHOW it to us!
Assuming a 3-flats key signature, and assuming there was an A natural accidental in the preceding bar, a cautionary Ab (with or without parentheses) is normal and correct. Where there are two 'voices' it is maybe a little pedantic to add it for each voice in piano music (it would be required in a vocal score where the different 'voices' actually WERE different voices.)
In any case, no, accidentals are not additive. A flat in front of A means A flat, no matter how many previous times we've been told A's are flattened.
