#1
If I were to record an acoustic paino with only one mic, what would be the best placement of the mic?
#4
This could be tricky to get right. Try the mic over the middle of the piano first with the lip open, then try it in various places, maybe pointing inside the piano, that could sound awful though.
#5
is it an upright or a grand piano?

with only one mic, no matter where you put it you wont get a balanced recording.
the strings nearest to the mic will be more present than the ones furthest away.

if you really cant get a spaced pair going, i;d say just place it in the center, lid open.
#6
is it a upright or a grand? I've got a book of recording techniques I can look at. Just say if its a grand or upright and I will go and take a look
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#7
Use your ears!
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#8
I would start with above the piano with the lid open
then try by where your head is when playing
Try inside the piano lid open/closed
try treble end
try bass end
try center
under the piano?
by the pedals? (then you get pedal noise, always thought that would sound cool)
side of piano?
back?

basically just what willieturnip said:
Use your ears!

-Ryan