For your first question my answer is yes.
For doing 32bit operation in 16 bit controller you can use double int are manually create a library which will do 32bit operations using 16bit instructions.
Mainly integer size is based on the compilers it will vary according to the compilers. Assume two different compilers can have different int size for a same microcontroller and vice versa.
you have to see the types defined in stdint.h, or otherwise gothrough the documentation of the compiler.