Sorry to say this is not a good precis. You have failed to understand parts of the passage(and therefore failed to reproduce them in the proper manner)

Literature is not only reflects life but age also.
Grammatically, it should be: Literature reflects not only life but also age.
From the point of view of the precis, the sentence is wrong. The writer is not talking about the age in years, but the age that refers to a time period(like the bronze age, industrial age).

In order to know history it is needed to read the books of the age
The passage says in order to understand the 'spirit' of that age, it is important to read the books 'read by' people of that age. Not 'books of the age' but the books read by people of that age.

It is supposition that the books we value and refer to the age were being valued by the contemporaries.
It seems correct, but i would add 'equally valued' instead of simply valued.

Literally the age and its history emerge gradually
Its clear you havent understoo the meaning. The passage says literary repute(of a book) is developed over time.

It is remembered that the reading in any age is the reflection of older age
Again you either haven't understood, or failed to reproduce the right meaning. The author is just saying that in any given age, people read the better books of an older generation. Your sentence says something else.