Electrons in Rutherford's gold foil experiment

They did.

The alpha particles are more than seven thousand times heavier than an electron.

Also, the alpha particles have a lot of energy, around 5MeV, and the first ionization energy of gold is about 9 eV.

Because of these, alphas can hit quite a few electrons without being affected too much. Think about a speeding school bus and a watermelon :)

(References: http://dept.astro.lsa.umich.edu/~cowley/ionen.htm and http://en.wikipedia.org/wiki/Alpha_particle#Energy_and_absorption)

Primarily because of the fact that a nucleus is much, much heavier than electrons are, and electrons are widely dispersed in an atom. Also, gold foil is neutral in overall charge hence it doesn't deviate the trajectory unless the alpha particles come quite close to the foil. The probability of approaching a nucleus is very low compared to just passing through the empty space. This is even lesser for the electron.