1. could the number 0000 appear in a table of random digits? how likely is this?

Yes,

probability = favorable outcomes/ total outcomes

to calculate the probability for this to occur, we use nCr ( nCr = n!/r!)

there are total 10 digits

so probability of the number 0000 appear in a table of random digits=

(1*1*1*1)/(10C1 * 10C1 * 10C1 * 10C1)

= 1/10000