Would some enlightened individuals please explain how having more hashing power than 51% will affect an attack?
Will the speed with which they can rewrite blocks increase?
Yes, higher hashrate means the attacker can close the gap faster. With 51% or 50.001% he is guaranteed to outpace the network from any disadvantage (say 6 blocks),
eventually. The guarantee doesn't tell you how long it will take, and in fact with 50.001% it would take on average about 6 years (it's random so it could be much less). With 51% it's 2 days. (These estimates are with a very simplified model, actual numbers could be different).
Could a 45% attack work if the attacker gets lucky by finding the correct hash before the other 55%?
Yes, he has a chance of success but no guarantee.