The sale in this sentence is a noun am I right? And if it is, is it singular due to sale is uncountable?
Yes, it's a noun. But it is countable. It is singular because sale is a singular noun.
For example, if I am a bad salesman I might make only one sale, but if I am a good salesman I might make many sales.
So, it is countable, but you used it correctly.
The sales vary.
In general, the sales for each of the items vary from one month to the next."
You could also say the number of sales varies.
The sales vary.
In general, the sales of books, stationary and toys vary from one month to the next."
The number of sales varies.
The sales vary.
You know what? You are great already. Even highly educated people who speak only English do not usually have error-free writing. So, you are already very, very good!
Oh! I just figured out what you mean. Yes, you can use sale as an uncountable noun.
In general, the sale of books, stationary and toys varies from one month to the next."
Here is how I would do it:
In general, the number of sales for books, stationary and toys varies from one month to the next."