Smooth infinitesimal analysis and law of excluded middle

Question

I read about smooth infinitesimal analysis and I have several questions:

1. How to prove that in SIA every function on $R$ is continuous? (Every function whose domain is $R$, the real numbers, is continuous and infinitely differentiable.)

2. What does "$ε.1$" and "$ε.0$" mean in this proof? (https://publish.uwo.ca/~jbell/basic.pdf , page 5-6)

3. For what purpose do we use Kock-Lawvere axiom when we deal with law of excluded middle? (https://www.fuw.edu.pl/~kostecki/sdg.pdf , page 21)

Thanks!