I have a Heil heat Pump brand new and a indoor unit. When system is off from the thermostat the outside unit fan is running non stop backwards. If I turn the a/c or heat on it stops then change direction and works perfect. The system works perfect all the time, it is only when is in off position the compressor stops and the fan outside changes direction. What could be the problem?

If it's brand new, call the installer. This should be handled under warranty.

I installed the system by myself! And forgot I have another problem. Cooling worked perfect the whole summer, but yesterday I put it on heat and it works perfect for 5 minutes and the indoor unit fuse 3 amp from the transformer blows. I changed the fuse and same thing happened, then I switch to cooling mode and no problem. Only the fuse blows when calling for heat. What do you think about this?

Replace the low voltage wiring between the indoor & outdoor units. If that doesn't help, you could have a reversing valve problem.