I know that I can't send even 1 satoshi due to dust transaction prevention, but the question is - might the transaction fee be not e.g. 160 satoshis, but 160.1 satoshis?
No, it's not possible. Transaction fees are not explicitly included in transactions: they are computed from the difference between the sum of the amounts of the outputs and the sum of the amount of the inputs . Since the smallest value that can be represented in an output amount is a satoshi , it's not possible to generate fees less than that.