Given that the Sun emits wide band RF noise at high levels, how is the Parker probe going to transmit its data collection to Earth (Terrestrial) when it reaches its closest proximity to the Sun in order for us to analyse?
It won't transmit data when it is at the closest points, but those periods are pretty small. Take a look at this image seen from this report to see how these will work. 1 degree can transmit Ka science data, 3 degrees can transmit X-band science data. The key thing to pay attention to on this chart is the green line, where it goes down to near 0 there will be no communication for a period of time. The spacecraft is more then capable of independently operating for this period of time.
In addition, during the very closest periods of time to the Sun the spacecraft is pointed in such a way to protect the spacecraft. This will prevent communication because the antenna cannot be pointed to the Earth during that period of time (Or at least not constantly)
Parker Solar Probe is designed to operate completely autonomously during the data collection periods of its orbits for exactly this reason - the RF noise from the Sun swamps reception. From here:
For several days around the Nov. 5 perihelion, Parker Solar Probe will be completely out of contact with Earth because of interference from the Sun’s overwhelming radio emissions.
So the probe collects data autonomously and transmits it later once it has moved further away from its perihelion.