What is the intensity of radio noise around Jupiter or Saturn on various frequencies compared to Earth? Does it significantly affect bandwidth for communication of satellites around Jupiter/Saturn with Earth? If yes, how is it solved?
The noise around Jupiter is quite significant. It is primarily around 40 MHz, according to this site, which teaches one to listen to Jupiter. This is not an issue for satellites around Jupiter/Saturn, as they use a much higher frequency (In the GHz range) to communicate with Earth, thus the radio noise doesn't affect them much. It releases these radio waves because of it's large magnetosphere.
Saturn doesn't have such a large magnetosphere, and so while it might emit some noise, it isn't considered to be a huge amount of noise. Jupiter, Earth, and the Sun are the largest producers of radio waves in the Solar System (And Earth isn't just because of humans).