The sine function has values between plus one and minus one so if you set A=1, all your samples will be small values. With a clean signal you should still be able to pick out the tone but it is a lot easier when the amplitude is larger.
I still have a lot of other numbers in other bins. Is that normal to FFT?
You have exhausted what I know about the FFT 
You can get noise in the resulting signal but it should be significantly lower than the tone you're looking for. I also get strange results with some signals and I haven't been able to figure out why it happens.
Pete