About rational Hodge conjecture. What progress has been made to date on the rational Hodge conjecture ? Can anyone tell us if there is some new books related to Hodge conjecture which explain in detail, the latest development in the field of rational Hodge conjecture ? Thank you in advance for your answers.

Donu Arapura's paper is quite good for your first question:

As for the second question, I would recommend James Carlson's "period mappings and period domains" which is very nice. And it gives several examples like HC holds for unirational fourfold. I am reading that book now