How can one full node know whether other nodes agreed a block suggestion of a miner (so it will know whether to add the block to its blockchain too)?
There is no guarantee that when a full node adds a block to its main chain that other full nodes have done so. However there is no need for a node to know that in order to add a block to its main chain; it simply has to validate the block according to its consensus rules before adding it to its main chain. If everyone follows the same consensus rules, then all nodes will converge to the same blockchain. The blocks in a blockchain are defined by the consensus rules.
Additionally, it is generally safe to assume that the peer that sent a node a block also added that block to its main chain. However that does not necessarily mean that a node should also add the same block; it must still verify the block because that peer could be following different consensus rules.