Solder paste is a paste made of solder. It is a bit wetter than toothpaste. It is applied to the pcb pads of surface mount components with either a paste mask and a squeege, like screening ink on a t-shirt, or a robot arm with a nozzle that deposits a very precise little dot. A paste mask is a thin sheet of steel (usually), photo-ethed with a hole pattern than matches all of the SMT device pads in shape and location.
Solder mask and solder resist are essentially the same thing, a coating applied to a pc board so than when it is hosed down with liquid solder, there are some areas where the solder does not stick. For example, a ling trace between two resistor pads does not need to have solder on it the entire length, only at the two pads.
Any conductor (pcb trace, hookup wire, bread knife, whatever) radiates both electric and magnetic fields. Most conductors are such a small fraction of the wavelength of the signal they are conducting that they make very inefficient radiators, but they do radiate something, always. You can optimize the shape of a conductor to make it a more efficient radiator at specific frequencies, but all you are doing is improving its efficiency; it was gonna radiate something anyway.
ak