What is the meaning of my fourier transform results?
The first entry [1] in the FFT is your fundamental, but the zeroth entry [0] is DC!

A standard FFT will have the same number of output samples as input samples, and they will all be complex. 

The results aren't necessarily symmetrical about DC. However in the special case of a real only input, they are complex conjugate about DC, which looks for all the world symmetrical if you take the power, or don't notice the sign of the imaginary part. Most FFT packages will have a special 'real input' mode which saves on processing time and array size by only producing the +ve half of the results when given a real input.

When you inverse FFT'd back, you were presumably using only the +ve half of the frequency coefficients. This will give you an analytic signal in the time domain. This is as you describe a sine and cosine, at right angles, with a constant modulus. The real input signal has both +ve and -ve frequency components, which the FFT separates. 

If you instead inverse FFT using the whole of the frequency spectrum, either by doing a full complex to full complex FFT to get the frequency coefficients, or by complex conjugate reflecting them through zero, you will reconstruct your original real time waveform (with some fiddling 1e-15s kicking around where there should be zeros due to finite precision). The IFFT of the +ve half spectrum produces the result you saw, the IFFT of the -ve half produces a similar signal with the cosines in phase, but the sines in inverse phase, so the resulting sum is pure cos and zero sine.