How long does it take to update all nodes that have the blockchain so that they are identical? Beginner questions...

I understand that everybody has their own copy of the blockchain. 

If one person makes a change, for example a transaction, I assume that it has to propagate to all other nodes. How long does this take?

How does a node know that the update process is complete throughout the blockchain?

What algorithm is used to synchronize and what is its order (O())?
The Blockchain is never changed only extended.

As I understand it, nodes do not explicitly check or care whether other nodes have identical copies. They just verify what they receive against what they already have in their copy of the Blockchain.

Synchronisation isn't exactly the right word to describe what happens but it effectively occurs as a consequence of nodes applying the same "consensus" rules. Nodes follow the longest chain, the one with most proof of work.