If time dilation approaches zero, could set particle fall into a black hole before it evaporates completely? Yes, that's an easy calculation. It's a little bit sut because when you have a black hole that doesn't evaporate, there is no event horizon really for an evaporating black whole. So that complicates things. What you can do is you can define an apparent horizon. There is a way with making reference to the future evaporation of the black hole. In that sense, that's where the hawking radiation is coming from. And yes, particles can pass in, pass by that apparent horizon, no problem, long before the black hole evaporates.