The set of integers is shown below.
The dot dot dots just means that the set of integers would also include -4, -5 and on down as well as 4, 5 and on up.
The set of integers includes the set of whole numbers.
For example {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...} are some of the whole numbers which appear at 0 and to the right of 0 on the number line.
The set of integers also includes {-1, -2, -3, -4, -5, -6, -7, -8, -9, -10 ...} which appear to the left of 0 on the number line.
To answer your second question, there is no integer that is the smallest.
Unlike natural numbers which are your counting numbers that start at 1, integers will never start of end. So they're is no integer that is the smallest or the largest.