Parking is already controlled at "market rate." In San Francisco parking can easily run over $20/day. If you can afford $20/day just to park your vehicle, then you should be able to afford congestion pricing, or else find an alternative (which would hopefully get you in to the city faster since there's less congestion).
No one said it has to raise revenue. This whole process could be revenue neutral. Give direct cash injections to the bottom 20% to offset the cost. This is about incentives, not revenue.
Ya, that is indeed the question. Just pointing out that it would in fact work.