Kolika as a number-pronoun is the genitive, dative, locative and instrumental case of kolik. So yes, it can also be "to how many/much".
Apart from that, kolika as a noun is a colic.
"Dej si." means "Give (it) to yourself.".
It is normally used for food in the sense "Have ..." but it doesn't really make sense for something you cannot eat or drink (or smoke).
In English translation wouldn't this make more sense as "To how many people did he promise that " ?
We do accept "How many people did he promise that to." and I added "To how many...".
But according to https://www.oxfordlearnersdictionaries.com/definition/american_english/promise_1 all of "promise somebody something", "promise something to somebody" and "promise somebody (that)" are possible. The "to" before "somebody" should not be necessary, although some reports claim otherwise.
Unless you parse it that he promised the people to some that...