1) DC-current will result in a constant magnetic field, the right hand rule can be used here. See https://en.wikipedia.org/wiki/Magnetic_field#Magnetic_field_and_electric_currents for more information on that. An electromagnetic wave is not "produced" in the steady state case, as we ignore the activation operation.
2) An AC-current will result in a alternating magnetic field. An alternating magnetic field will cause an alternating electrical field and voila - you just made an antenna and will send electromagnetic waves. Anyhow, its a very bad antenna, but there are a lot of tricks to make them better.
3) Is the same case as 1)
4) An accelerated charge will always result in bremsstrahlung, see https://en.wikipedia.org/wiki/Bremsstrahlung for more information on that.