how does a block know that its transactions have tampered with in the first place?
It is not the block that knows this; it is the nodes which verify that.To quote the bitcoin whitepaper:
When a node finds a proof-of-work, it broadcasts the block to all nodes. Nodes accept the block only if all transactions in it are valid and not already spent.
and
[...] network nodes can verify transactions for themselves
So, the nodes verify the transactions upon receiving a new block. This adds to the blocks confirmation counter (you can see it in here, for example), hence making it more trustworthy.
To answer your question directly, yes, the blocks get recalculated regularly.
This is not much of a problem for a node however, since it needs only one hash (the nonce is already known) to verify a block, which is vastly easier than calculating a proof-of-work. Same goes for verifying transactions. Exactly how many transactions are verified is something which I don't know myself, might be a topic for another question.
When a node "notices" that a block is invalid, it discards it and can even
[prompt] user's software to download the full block and alerted transactions to confirm the inconsistency.
You might also find this thread quite informative: Bitcoin transactions validation process