On Bitcoin's Blockchain, how is information transmitted instantly to all other nodes and do nodes 'talk to each other' through an API?

Information is not instantly transmitted. It takes time, nothing is instant.

The Bitcoin network has a network protocol which nodes using it speak. This network protocol allows a node to send and receive data to and from a node that it is connected to. A node will connect to multiple other nodes on the network.

This network protocol uses TCP connections and Bitcoin specific network messages.

Do Blockchain nodes communicate with each other through HTTP requests?

No. That would be inefficient.

Or is there a delay until the full blockchain information reaches all nodes?

Of course there is a delay, the speed of light is only so fast. Data takes time to transmit due to the capabilities of physical connections and the distances that information has to travel. There is always a latency due to physics. Furthermore, Bitcoin nodes will have random delays between each of their announcements of transactions in order to better preserve privacy.