As to the first, the banks officially resumed specie payments, i.e. they declared themselves ready to redeem anyone’s notes in specie on demand. However, Rothbard says here, that the banks have increasingly tried to put obstacles and intimidate those who attempted to press the banks for payment in specie. Hence the ‘more nominal than real’.
In the second point, Rothbard speaks of a loss of confidence. Even in regular times, some people would demand specie, and the more the banks expanded their notes, the more specie from their reserves would be requested, putting them on a shakier ground. Their unwillingness to produce the specie despite official guarantees could alone inspire a certain lack of confidence, hence the premium for specie in the market.