How long does block validation take?

How long does block validation take?

Assume a miner receives a new block from a connected peer. Please correct me if I'm wrong: The miner validates the newly received block before using it themself and sending it to their other connected peers. I heard this but it seems to me that it'd be a better strategy to already use the block to mine on top of it because the block header and the proof of work associated with it is very fast to verify and it's highly unlikely someone made a block header with a small hash for an invalid block. So why keep mining on top of the previous block?

How long does this process typically take? What does it depend on? Is it done on specialized mining hardware or on a general-purpose CPU?

Is it correct that the time block validation takes is linear to the block's + witness's size should segwit activate?

Also: How long does it take on average for a block to be propagated through the network? It'd be great if that average is weighted on the receiving miners' hashing powers.

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