[paul.fr]

If we sent a probe to the sun, sending back radio and video signals. At what point would we lose contact with the probe, and at what point (distance from the sun) would the probe melt from the heat?

[syhprum]

At the distance of the Earth the radiation amounts to about 1.3 KW /sqr Meter and of course increases according to the inverse square law.
The temperature of the probe would depend on how reflective it was but at a guess I would say you could work to about 1/20 of the Earth-Sun distance.
In close proximity to the Sun there would be other forms of radiation against which the probe would have to be hardened.
I do not think communication generally would be a problem but as the probe will be orbit the Sun with a period of four days alignment of the transmitting antenna may present problems