Re: 8-bit, 16-bit and so
That refers to the number of bits it can process at a time.
An 8-bit micro for example, works with 8-bit quantities. That is, most operations (addition, subtraction, AND, OR, etc.) are performed on 8-bit numbers. Most registers are then 8 bits wide. To perform operations on larger numbers, requiring 16, or 32 bits, for example, you need to write code to handle that on a byte-by-byte basis. That involves additional instructions, to handle each byte, plus instructions to deal with eventual carry, overflow, etc.
It's like you adding two numbers, in decimal. 5+4=9. That is easy. But if you need to add 65+54, then you first add 5+4=9, check if anything carries over, if not, then you add 6+5, and 1 carries over. You then write the result remembering the order of the digits in the result, which is also important. That operation was now much more complicated, wasn't it? If the numbers are even larger, you need even more additions and checks.
So you can see that the larger the number of bits a micro can handle at a time, the faster it will be, since you can handle large numbers in just one instruction, without any additional software overhead.