No, it won't. The Whip doesn't add haste to the Rat's copiable characteristic values; it just creates a continuous effect that gives the Rat haste. A copy of that Rat won't have haste.
You might be thinking of effects that create tokens (like Minion Reflector), but those are different because effects that create tokens can also set their copiable characteristic values.
110.5b The spell or ability that creates a token may define the values of any number of characteristics for the token. This becomes the token’s “text.” The characteristic values defined this way are functionally equivalent to the characteristic values that are printed on a card; for example, they define the token’s copiable values. A token doesn’t have any characteristics not defined by the spell or ability that created it.
Yes, the token will remain on the battlefield. Only the creature that was Whipped back will be exiled. Any tokens made by it remain on the battlefield.
Private Mod Note
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Rollback Post to RevisionRollBack
DCI Level 2 Judge
Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.
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What abilities get copied?
Will it have haste?
GB Electric Dreams BG Deal 20 in one shot, or discard their hand?
GWU Free Stuff Midrange UWG Slowly bury the opponent with more threats and answers than they can handle.
My greatest hits:
GURFate Reforged Temur Ascendancy COMBORUG
GUDragons of Tarkir Whisperwood Forever UG
You might be thinking of effects that create tokens (like Minion Reflector), but those are different because effects that create tokens can also set their copiable characteristic values.
Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.