My A/C is blowing hot air inside, but the fan will not run outside the house. When I turn the breaker off then on again the fan will start up for about 10 seconds and then trip the circuit again.

You have a short somewhere outside in the outside unit. Or the fan motor is going or gone.

The unit is only a year old in a brand new house, with new wiring.
We already had to get the contact changed a few months ago. Is this normal for a new unit to have so many problems?

No. New units that are properly sized and installed do not have these problems. Get a professional (a trusted one) to thoroughly test each components to see which went bad. Also, if this is just a new unit, definitely contact the manufacturer to see what they say. It could still be covered under a warranty with them.

Yes it is still under warranty. The company who installed it is horrible at getting back to you especially because it is under warranty. I really hate dealing with them. I was just poking for answers/questions I could ask them when they come to fix the unit. I'm getting sick and tired of dealing with these people.