Does bitcoin stop periodically for finalising the next block?
No, block discovery is a memory-less process. Every try of discovering a valid block is completely independent from any other. Miners continuously search for a new block. The only thing that changes over time is which transactions they're trying to include and what preceding block they are building on-top of.

When some miner finds a block that fulfills the required criteria, they just publish it to the network. The propagation of the new block also works as the signal for all miners to switch work to a successor of this block instead of the predecessor.

Transactions are relayed in the network independently and continuously. Miners may update their block template to include new juicy transactions every once in a while, but it's up to them how often and when they do this.