Does the sun's electromagnetic field disrupt communication? If you were to design a drone or probe that could fly close enough to the sun to examine the corona, closer than the Parker Solar Probe, how close could you get and still have reliable communications with it? Is there a point where the sun's electromagnetic interference would make it impossible? This is assuming that the drone has adequate heat shielding. If radio communication fails would something like a laser communications system still function?
 A: 
Does the sun's electromagnetic field disrupt communication?

Yes, definitely. Even as far away as earth, there can be a noticeable effect on shortwave (HF) radio communications - the Wikipedia article on space weather says

At auroral and polar latitudes, small space weather events that occur frequently disrupt HF communications. At mid-latitudes, HF communications are disrupted by solar radio bursts, by X-rays from solar flares (which enhance and disturb the ionospheric D-layer) and by TEC enhancements and irregularities during major geomagnetic storms.

During its closest approaches to the sun, the Parker solar probe is already at the point where radio communication with earth is unreliable, and it has to operate autonomously for several days at a time:

The near Sun radiation environment is predicted to cause spacecraft charging effects, radiation damage in materials and electronics, and communication interruptions ... Within each orbit of the Parker Solar Probe around the Sun, the portion within 0.25 AU will be the Science Phase, in which the probe will be actively and autonomously making observations. Communication with the probe will be largely cut off in that phase.

