(theoretical) doubt in Gauss law
Gauß' law says that a charge inside a volume generates a total flux through the surface of that volume. It also implies that external fields do not contribute to this flux. Simply saying: external flux will enter the volume on one side, and leave on the other, resulting in no total flux.

Now, you're speaking about the universe and finding its center, which is a story on its own. Let's assume a sphere with uniform charge distribution \$\rho\$. And we will use spheres as volumes / surfaces of radius r as it's a symmetrical problem. Then, you get

$$E\cdot 4\pi r^2=\frac{1}{\varepsilon_0}\rho\cdot \frac{4}{3}\pi r^3\quad\Rightarrow\quad E=\frac{\rho}{3\varepsilon_0}\cdot r$$

This is the E-field generated by the uniform charge distribution enclosed by the sphere, directly at the surface. For an infinite sphere, the field will be infinite, too.

Another one:
Think of a sphere or radius R and charge Q. Outside the sphere, the field is

$$E\cdot 4\pi r^2=\frac{1}{\varepsilon_0}Q\quad\Rightarrow\quad E=\frac{Q}{4\pi\varepsilon_0}\cdot \frac{1}{r^2}\quad for \quad r\ge R$$

Inside, you have to replace the full charge by the charge enclosed by Gauß' surface, the fraction is defined by the volume:

$$\frac{Q'}{Q}=\frac{\frac43 \pi r^3}{\frac43 \pi R^3}\quad\Rightarrow\quad Q'=\frac{r^3}{R^3}Q$$
and so

$$E=\frac{Q}{4\pi\varepsilon_0}\cdot \frac{r}{R^3}\quad for \quad r\le R$$

Finally, I don't see any problems with Gauß. I guess you just forget that point about external fields.