Why do macro black holes take ridiculous amounts of time to evaporate—unlike micro black holes which dissolve in even less than a second? Why do macro black holes take ridiculous amounts of time to evaporate, considering that micro black holes dissolve in even less than a second?
Does this mass-based behavior imply that the matter within black holes still affects them with some of its physical properties even beyond the event horizon?
 A: Larger black holes are colder. The more stuff you throw into it, the colder it gets. 
This might seem counterintuitive, because for a familiar system like a balloon filled with gas, adding energy increases the temperature because it increases the kinetic energy of the molecules in the gas. But for a "gas" of astrophysical objects interacting with each other gravitationally, like in a cluster of stars (where the distances between the stars are large enough to justify treating them as "atoms"), adding more energy to the system makes it colder, in the sense that it decreases the average kinetic energy of the stars. This is related to the fact that a satellite in a higher-altitude orbit has more total energy (potential + kinetic) than an equal-mass satellite in a lower-altitude orbit. To move the satellite from a lower circular orbit to a higher one, you have to add energy, and it ends up moving slower.
In other words, the heat capacity of such a system is negative: adding energy makes it colder. Here's a related post:
Explanation for negative specific heat capacities in stars?
As explained in more detail in that post, the temperature of a black hole is $T\propto 1/M$, where $M$ is its mass. This says that a black hole has negative heat capacity: adding more energy (more mass) makes it colder. Conversely, as it gradually loses mass by evaporation, it becomes hotter and hotter, which makes it evaporate faster and faster.
Regarding whether or not the stuff "inside" a black hole can still affect its physical properties, that's a segue to the Black Hole Information Paradox, which still a very active area of (theoretical) research. 
A: One way of looking at Hawking radiation is to think of the usual representation of virtual pairs as oysters, upon which the BH can feed (losing weight in the process, of course). But it is the tidal effect, the gravitational gradient (GG), which allows the BH to separate the virtual pair, eat one and spit the other out. 
Think of the GG then as an oyster-shucking knife.
Now paradoxically the smaller the oyster, the larger its mass-energy, and the sharper the GG  must be to open it. Large BHs with big dull knives can only eat large low-energy oysters, and thus lose weight slowly, in the form of low-energy radiation. But small BHs can feast on high-energy small oysters- thanks to a sharp GG- and lose all their mass in a blaze of glory- UV,X, and gamma rays (some of which we may glimpse from billions of LYs away). 
This is an explanation I devised for a grandniece, and as such is hardly science. But she readily understood it, and I think it does have a certain intuitive appeal. 
