What is the magnitude of the impulse function at t=0?
The "impulse function" is not actually a function but a distribution, and its value at $t=0$ is not defined.

The impulse only really makes sense when multiplied by a signal inside an integral, where it is used to "select" the value of the signal at specific time instants.

Personally, I try to avoid impulses whenever possible. Look for Lapidoth's book on digital communications (available for free on his website) for a complete treatment of Fourier analysis (as relevant for communications) without a single delta. Not many people share my squimishness with deltas, though, and if you're taking a signals course they are pretty much unavoidable.

Note also that, once you go to the discrete time domain, everything becomes nicer: instead of the Dirac delta, you use the Kronecker delta, which is a regular function and has a value of 1 at $n=0$.