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

Yes. Demigods can تاریخ as long as their Immortal parents aren't the same.
A child of Hermes can't تاریخ another child of Hermes.
But
A child of Hermes can تاریخ 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 تاریخ somebody with the same godly parent. But even that seems like مزید 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 Lost 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 سے طرف کی Drew that children with the same godly parent can date, but they don't simply because of the weirdness factor.