Is “hour” a countable noun? Is it an abstract noun?

It is a countable and abstract noun.

A noun is countable if it has plural form and it can be used with numbers and word hour fulfills these conditions because you can say for example:

I spent two hours reading this book.

It is also an abstract noun because it does not describe any material thing but just an idea of a unit of time. If a noun is not abstract, then you can describe its physical properties like shape, colour, material and so on.