Why genes are assumed to follow multivariate normal?
Usually if something is not expected to behave according to some scheme then the measured values for such a parameter are assumed to be normal. It is not just with gene expression but with all types of measurements like dimensions of an object, luminosity of an electric bulb, range of a bullet etc. 
In any measurement, the random error is modeled using normal distribution. I don't have a very intuitive explanation for why random errors follow normal distribution but mathematically it comes from the central limit theorem. 

Now each gene is a variable and measurement of each gene suffers some random error; so a multivariate normal distribution is used. 

When we dismiss a null hypothesis in a t-test or z-test what we are actually doing is dismissing our parsimonious notion that a sample is drawn from a given normal distribution. This means two things:


The sample belongs to some other normal distribution (different $\mu$ and $\sigma$)
The sample follows some other distribution


But a t-test will never be able to point out the exact reason. All it tells you is that the sample is not from some given normal distribution.