I am a little confused - can I transfer foreign currency into my Monzo account in order to change money when the exchange rate is really good, or does this not make sense?
You can certainly use Currencies Direct to transfer foreign funds into pounds in your Monzo account, and vice versa.
You will only be able to take advantage of currency fluctuations if you can accurately predict them. If you can do that more often than not, I can guarantee that you are in the wrong job. And don’t forget that there will be some losses to overcome every time you change from one currency to another.