What block had the most transaction fees? Why? How big can transactions be? What's the largest transaction (size, in bytes)?
I am not sure which block it is, but you can see it on this graph from blockchain.info. It was ~305 BTCs in transaction fees. The blockchain will not tell you why the transaction fees are so high. It is probably an accident or a joke.
I believe the largest size a block can be is measured in terms of bytes, and it is 1MB. So the largest transaction can be as large as 1MB of data will let it be.