Defining the surface gravity of a black hole

Consider the following two definitions of the surface gravity of a black hole (taken from page 23 of Thomas Hartman's lecture notes on Quantum Gravity):

1. The surface gravity is the acceleration due to gravity near the horizon (which goes to infi nity) times the redshift factor (which goes to zero).

2. If you stand far away from the black hole holding a fishing pole, and dangle an object on your fishing line near so it hovers near the horizon, then you will measure the tension in your fishing line to be $\kappa M_{\text{object}}$.

What does it mean for the acceleration due to gravity near the horizon to go to infinity?

Why do we multiply by the redshift factor and what does it mean for the redshift factor to go to zero?