The input cap has the - terminal looking at the input, so if you put +5 on it....or +2, or whatever, you reverse bias the cap. At a minimum, it will behave terribly as a cap when the voltage swings positive. The + terminal is sitting, more or less, at ground potential. I don't know what you're asking how I get the voltage "across" the cap. One end is looking at ground, and the other end is looking at something other than ground.
No.
Whatever voltage you put on the input, the other end of the cap will have the
same. Hence, the voltage
across the cap will be 0V.
OK, after a while, the charge on the capacitor will change. But how long is a while? Well, to get an idea, let's calculate the time constant: 10uF times 100k is
1 second.
What is the period of the lowest audio frequency? Let's say 50ms (20Hz). So, with a healthy 20Hz sine wave playing into this, the capacitor doesn't have
time to significantly alter its charge during the positive-going part of the waveform.
To prove this, get a dual input scope and connect probes either side of the cap. You will see exactly the same waveform on each side - perhaps with a small DC offset. Case closed
Above, when working out the time constant, I said 100k. Was that fair? Yes, it is. The positive end of the capacitor sees 100k to ground, plus whatever the op-amp presents.
Earlier I quoted the first "golden rule" of op-amps: the inputs are always at the same potential. The second "golden rule" is that the inputs draw no current. In other words, the input impedance is extremely high (and is further raised by bootstrapping because of NFB).
To answer the second question I posed: if you place 5V DC at the input such that the capacitor "saw" the wrong polarity (which - having just re-checked the schematic - would be +5V, not -5V - sorry!), then that would be in series with 100k. The worst-case current would be tiny: just 50uA. Would that damage the cap? Based on my experience, I very much doubt it.
I've seen dozens of 40 year old capacitors with 3 or 4 volts of incorrect polarity (caused by a silkscreen error), and they've always checked out fine - I don't even bother to change or reverse them... (I can provide more details if you like)