Can you isolate a system from conduction and convection, but not radiation? Can you create a 'box' that isolates the inside from conduction and convection, but lets infrared and visible light pass? 
 A: You mean like a Dewar or Thermos bottle? 

They usually have silvered glass to reduce heat transfer by radiation, but you could omit or remove that to let as much radiation through as you'd like.

The long neck is to support the weight, while greatly reducing conduction along it.  You'll also sometimes see baffles inside the neck to reduce the possibility of convection there too.
A: Certainly. This is how solar heat collectors work. You surround the thing you wish to heat with double-paned glass windows. Visible and (some) IR go through the glass by radiation, and the glass blocks conduction and convection losses. 
Please note that when the object inside the glass box gets hot enough, it will begin to re-radiate in the infrared, and if the glass used in the construction of the box happens to be transparent to IR then you'll start to lose some of the heat that you have collected. This means that for best performance, the glass itself has to be chosen to minimize this. The tradeoff then is that if the glass blocks IR losses, it also blocks incoming IR from outside. 
The IR re-radiation rate scales strongly with the temperature of the hot object (as T^4) so if the temperature rise is moderate and not extreme, then those losses will not prevent this technique from working. 
