1. There’s extra danger every time nuclear material is launched on a satellite, be it for a thermal generator like on the Curiosity rover, or some failed tests the USA did on Pacific islands in the 60s as part of Operation Fishbowl that resulted in a large amount of waste spread downwind.
2. No satellites can actually reach the sun - to do so, anything launched from Eart would need to cancel the forward velocity to force its orbit to “fall” into the Sun. This is such a high number that it’d be cost prohibitive for the amount of fuel and size of launch vehicle required.