Does a variable with different range for rows affect the classification model
The first solution is valid. You need to keep the same unit for all rows per a given feature. But for currencies, you should be careful about the rate of conversion which might be dependent on the date of the data collection.

For the second solution, I am not quite sure about your end application but you may use it if you are trying to incorporate the effect of currency type in your model prediction. But if you are proposing it as alternative to the first solution, your model will less likely to infer the conversion rate among the various currency types.