My house is less than 2 years old. But the 1 year warranty is over.
Living room lights / fan do not have power most of the time. I double
checked the circuit breakers. They are all in the ON position. There
are a couple of switches in the circuit breaker. They have a green
TEST button. If I hit the TEST button, sometimes power comes in living
room on even if the switch is left in the off position or middle
position. The power is on for a variable time. Sometimes, it goes off
quickly. Other times, it stays for a few hours. Also, the fan and
light switch or not independent. If I turn off the light switch it
also turns off the fan. If I turn the light switch back on, the fan
turns on. For fan to work both fan and light switches must be on. For
light to work, only the light switch needs to be on.

What is the purpose of the circuit breaker switch with green "TEST"
button? Why does hitting the TEST button and leaving it in "OFF" state
bring the power on? I thought that the opposite would have happened,
meaning power will go off. What could be problem with my electrical
connections?

The electrical company that my builder used is asking for $75/hour to
come and look into this problem. They will also charge $150 for travel
on top of this. Should I have to pay them, even though it seems that
they did not do the connections correctly in the first place?