As far as I understand, there is technically a coefficient κ in front of the FT and IFT---κ2π in front of the FT and 1κ in front of the IFT. When I spoke to Professor Ivrii about this, he said that as long as we maintain the same value of κ throughout our answers, we should get full marks. But perhaps Professor Ivrii can further clarify this.
In reference to problem one, we need the FT to be unitary, which would require us to choose a value of κ=√2π, I believe.