Yes. Natural numbers are the counting numbers we use. Integers however contains also the negative values. So yes, natural numbers are integers, but the converse is not true though: integers are counting numbers is false.
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Fractions are not integers. They may or may not be rational numbers.
There is no single commonly accepted definition for "whole numbers". Depending on the definition used, zero, as well as negative integers (like -1, -2, etc.) may, or may not, be considered part of the "whole numbers".
Natural numbers are sometimes defined to include zero, sometimes not. Equivalent terms therefore may include: positive integers, non-negative integers, whole numbers, positive whole numbers ("whole number" is ambiguous; some take it to include negative numbers, some not).
8 and 10. Since they are integers, they may not include decimals, so the answer is simply just the numbers you would find by adding or subtracting 1.
The basic idea is the same as when you estimate sums and differences of larger numbers (which may or may not be integers). You round the numbers to one or two decimal digits, then add them up.