Nyquist Frequency Confusion 1- If I have a sine wave with period of $T$, I need to sample at least every $T/2$ to be able to reconstruct the sine wave. Let's look at this:



This way I'd get a series of $0$s and all information seems to be lost. Where am I wrong? 
$x(t)=\sin(2\pi ft)$

Let $f_s=2f$; then

$$x[n]=\sin(2n\pi f/2f) = \sin(n\pi)=0.$$

2- Assume I have sine wave of frequency say $100\text{ Hz}$ , and I sample it at $101\text{ Hz}$, this would cause aliasing as we know. My question is, what happens in the frequency domain?
For the number of samples given, your initial statement is false.  Sampling at exactly T/2 is a mathematical limit.  

For any finite number of samples, you need to sample a band-limited pure sinusoid of period T more frequently than T/2 to avoid aliasing or other pathologies, or at greater than 2X the highest spectrum frequency (for a baseband range). (and in real-life, to take into account the transition bandwidth and stop-band of any low-pass anti-aliasing filtering).  The shorter the sampling interval, the higher the sample rate needs to be above 2*Fmax (for a given baseband band-limited range) to reduce numerical, quantization, and other signal-to-noise induced errors to below some given threshold.

As you approach an infinite number of samples (beyond the life of the universe), you approach being able to reconstruct a sinewave with sampling at T/2.