Are Big Three's child actually cousins? Can they date?

Yes. Demigods can 日期 as long as their Immortal parents aren't the same.
A child of Hermes can't 日期 another child of Hermes.
But
A child of Hermes can 日期 a child of Athena.

It works with all Half Blood. As long as the person's Immortal Parent is not the same, they can form a relationship.

Everybody is related in Greek mythology.
Anyways, the rule is don't 日期 somebody with the same godly parent. But even that seems like 更多 of a mental thing, if gods don't have DNA and can change their appearance at will (Which would mean a change of DNA if it existed) then the negative effects of such pairings is negated.

They actually explain this pretty well in The 迷失 Hero, with Jason asking a similar question. Because gods don't have DNA, their children technically aren't related to any of the other Olympian children. It is somewhat implied 由 Drew that children with the same godly parent can date, but they don't simply because of the weirdness factor.