>>My problem is, how do you tell (electronically) when someone picks
up the phone at the other end after placing a call?

I battled with the same problem.  I found that in some cases the line
current reverses on the caller side as soon as the call is answered.
In these cases, you then have an accurate starting point.  I use two
opto-isolators with the diodes in series with the line and in
parallel with each other (facing opposite directions) to sense this.

I use a call progress tone detector to deal with the case where the
line current doesn't reverse - the CML FX633.  It's an 8 pin device
with a pin that goes high if there's a valid tone (ringing, engaged,
no-longer-exists, etc). So if I don't see a valid tone for 2 seconds
(the time between two rings) and there's still line current, then I
assume the call is answered. It's fairly immune to noise, and human
whistling etc.

I initially tried to build my own filter (looking for the 400Hz
signal) but it lacked the gain control & noise immunity.

There are still the problematic cases where the call is answered
before the caller even hears a ring.  And when the line is noisy, the
tone detector battles.

Let me know how you get on - my system needs improvement.

Cheers
Rob