For 8 bit platforms, 8 bits are still bytes/sbytes. Most of them have native functions that work on 16 bit integers, they just take up a pair of registers. You have access to the same array of integer sizes. Plain int is 16 bits, and longs are 32 bits and long longs still 64. Still, I much prefer using the int definitions included in C99, where you define the bit size explicitly. uint16_t is a lot more explicit than int, especially if you've got code that's being shared between a few different micros of different word sizes.

On AVR 8 bit microcontrollers, at least: yes. Pointers are 16 bits, and there are a handful of instructions specifically for 16 bit integer and pointer operations (which operate on pairs of 8 bit registers). For everything else, operations are performed by chaining together 8 bit operations. Adding two 32 bit ints for example would need 4 add instructions.