How to program ATTiny85 running 3.3V
Since the ATTiny can easily run at 5V I don't see any problem with programming it at 5V levels and then run it at 3.3V. Is that correct?


Yes. But if there are any components on the board that can't run at 5V then you must provide some way of protecting them from the excessive voltage.


  If I change the fuses on Tiny to run it at 3.3V can I still use the 5V Arduino to program the tiny?


There are no fuses required to change the actual operating voltage of the device. There is the BOD threshold, but you can still operate the device at a higher voltage without issue regardless.