I've read that Jupiter emits a lot of EM radiation, and can also be heard on ham radio. If you were much closer would it drown out radio and other forms of communication, or is it confined to specific frequencies?
There are multiple sources of radio emissions in the Jupiter system, but the most powerful are the jovian kilometric, hectametric, and decametric emissions in the 0.1-40 MHz range arising mostly from the Cyclotron Maser Instability mechanism, and synchrotron radiation in the 0.1-15 GHz range, peaking somewhere around 0.3 GHz (300 MHz). Both of those mechanisms arise from Jupiter's powerful radiation belts. Both are "broadband", i.e. not confined to narrow frequency ranges.
Multiple spacecraft have successfully used radio communications from the jovian system to Earth. The Galileo Probe (also here) successfully sent data through the highest-energy source region of the synchrotron radiation to the Galileo Orbiter spacecraft, so useful radio communications can indeed be done despite the noise environment. You just have to design the radio system for it.
One important aspect of that design is the bandwidth of the receiver, the range of frequencies it receives. The narrower that bandwidth, the less noise it gets. But the bandwidth must be wide enough to carry the data being sent: required bandwith is roughly proportional to the radio link's data rate.
And supporting that data rate requires a certain level of signal-to-noise ratio (SNR), i.e. the signal received must be at least a threshold level more powerful than the radio noise received. In the design phase of the mission, when the required data rate sets that required bandwidth, attaining the necessary SNR can be done by such approaches as increasing the transmitter's power, changing frequencies to one with less noise, or arranging (via clever trajectory design or timing) to have the receiver closer to the transmitter.
The Galileo Probe had an additional hurdle to clear: the ammonia in Jupiter's atmosphere is a strong radio absorber. Water is also a radio absorber but is weaker than ammonia—but there is more of it. Above ~0.3 GHz Jupiter's synchrotron noise power decreases with increasing frequency, and the great majority of spacecraft comm systems operate well above 0.3 GHz. But in Jupiter's atmosphere the absorption by ammonia and water increases with increasing frequency. The Galileo Probe chose a frequency, "L band", ~1.387 GHz, where the combination of the two—noise and absorption—gave the best data rate for the transmitter power they could afford.