If you were living in US (before June 24th) and travel to Nepal (for short period), you can still apply TPS. But if you are coming for the first time after June 24th, you are not eligible at all.
AP will let you travel as many times as you want without any issues (I have friends from African countries with TPS, they are doing all the time). Its not recommended to travel if you have asylum application pending or have criminal background.
One of my friend was in Nepal for his marriage during Earthquake and he came after June 24th, when he consult a lawyer, he is still eligible to apply TPS.