Why is the electric field zero inside a hollow conducting sphere?

If the shell and its charge distribution are spherically symmetric and static (which your question does imply when you say "uniform charge"), and if electric field lines begin and end on charges, then we know that any electric field that might be present inside the shell must be directed radially (in or out, i.e. $E_{theta} = E_{phi}=0$).

From there, a simple application of Gauss's law, using a spherical surface centered on the center of the shell tells you that the radial electric field component must also be zero at any radial coordinate $r$ within the sphere. $$ oint vec{E} cdot dvec{A} = frac{Q_{enclosed}}{epsilon_0} = 0$$ $$ 4pi r^2 E_r = 0$$ $$rightarrow E_r = 0 $$

Therefore, we can say that at any point within the sphere (defined by $r$ and two angular coordinates) that $E_r = E_{theta} = E_{phi}=0$ and so the total electric field at any point (inside the sphere) is zero, not just the centre.

if you consider an off-center point,the field created by the charges near to the point should be equal to the field created by other charges sitting opposite to it. Amount of charge and distance varies will prove this field or field strength is same. As they are opposite the net field is zero at any off-center point.